title: Óscar Valdez

text: Valdez made his first title defense against 31 year old Japanese boxer Hiroshige Osawa (30–3–4, 19 KOs) on the undercard of Pacquiao-Vargas PPV bout on 5 November 2016. Osawa was ranked #1 by the WBO. The fight took place at the Thomas & Mack Center in Paradise, Nevada. Valdez told FightNews.com of his excitement for his first title defence, “I am excited for this fight. I am looking at this fight like if I am the challenger and I want to keep that mentality to do my best and win the fight. I am ready for my first title defense but I am still training like I am trying to win that title.” The fight was one sided fight, Valdez halted Osawa in round 7 when he hurt him with a hook followed by a barrage of shots that prompted referee Vic Drakulich to stop the fight. Valdez hit accurate jabs and hard shots to the body and head from the opening bell and managed to knock down Osawa in round 4. At the time of stoppage, Valdez was ahead 60–53 on all three judges scorecards. According to Compubox, Valdez landed 191 punches to only 35 by Osawa, which included 129 power punches to his Osawa's 18.


title: Óscar Valdez

text: On 17 February 2017 Top Rank announced that Valdez would be making a mandatory defence of his WBO featherweight title against former WBA 'Super' World featherweight title challenger Miguel Marriaga (25–1, 21 KOs) in the main event at the StubHub Center in Carson, California on 22 April 2017. Marriaga knocked out Guy Robb in August 2016 to become the number one challenger. Bob Arum confirmed the undercard card would also include Gilberto Ramírez and Jessie Magdaleno defending their respective WBO titles and Olympic silver medalist Shakur Stevenson making his professional debut. In front of 5,419 fans, Valdez retained his WBO title in a slugfest, but was taken the 12 round distance for the first time in his professional career. It was also the first time in six fights going back to June 2015 that Valdez had a decision victory. The final judges scorecards were 119–108, 118–109 and 116–111. Many at ringside believed the wider scores did not do Marriaga any justice as it was a back and forth action fight. Marriaga was knocked down in round 10 after some strong middle rounds.


title: Óscar Valdez

text: In July 2017, Top Rank set a return date of 22 September 2017 for Valdez to make a third defence of his WBO title. His manager Frank Espinoza confirmed that he was back in training. A venue in Tucson, Arizona was discussed. On 9 August, it was revealed that Valdez would fight unbeaten Filipino boxer Genesis Servania (29-0,12 KOs) in a voluntary defence at the Tucson Convention Center, with Gilberto Ramírez once again co-featuring. Valdez stated that he would like to unify the division and fight the winner of Leo Santa Cruz and Abner Mares, which was likely to take place in the fall of 2017.


title: Óscar Valdez

text: In front of a crowd of 4,103, Valdez managed to recover from a knockdown and score a knockdown of his own, en route to retaining his WBO title via unanimous decision after 12 rounds. The three judges scored the fight 117-109, 116-110, 115-111 in favour of Valdez. Servania dropped Valdez in round 4 with a right hand to the head. Valdez recovered, but looked visibly hurt as he tried to shake it off. Servania was dropped following a big left hook the very next round. After round 6, the fight became one-sided. Servania struggled to let his hands go. After one punch, Valdez would grab Servania in a clinch. Valdez began to work the jab and throw power shots until the closing bell. In the post-fight interview, Valdez shrugged off the knockdown, “I never thought I was gonna be on the canvas like that. But this is boxing. To be completely honest, I wasn't really hurt. I was really surprised. I was like, ‘OK, I’m on the floor. But now, I’m gonna get up and I’m gonna do my work.” Valdez managed to land 192 of 697 punches (28%), he earned $400,000 for the fight, while Servania, who earned a $55,000 purse connected 120 of his 450 thrown (27%). Servania seemed upset with the wide scorecards, felt it was close and was open to fighting Valdez again. The whole averaged 706,000 viewers on ESPN.


title: Óscar Valdez

text: Top Rank stated they were planning to have Valdez back in action in February 2018, and hoped to have him fight three times during 2018. On 28 November 2017, according to "RingTV", Valdez was to make his next defence on 10 March 2018 at the StubHub Center in Carson, California, headlining a Top Rank card on ESPN. On 3 January 2018, ESPN first reported that a deal was close to being reached for Valdez to defend his WBO featherweight title against British boxer Scott Quigg (34-1-2, 25 KOs). On 13 January, the fight was finalized. Valdez came in at 125.8 pounds at the weigh in for his fourth defence. Quigg however came in 3 pounds over at 128.8 pounds. He was not allowed to re-weigh. According to the California State Athletic Commission, if a fighter is 2 pounds or more over the contractual limit, he would not be allowed to lost the extra weight as he would have been 'dried out', any more weight loss could potentially be dangerous to their health. The CSAC fined Quigg 20% of his official purse of $100,000, with Valdez receiving half of the money from the fine. Quigg's purse was believed to be far more at around $500,000 plus British TV rights. Valdez was due his highest purse at $420,000, not including the additional $10,000 from Quigg's purse.


title: Óscar Valdez

text: After a hard fought 12 round battle with saw Valdez break Quigg’s nose and in return Valdez have his own front teeth damaged, the final scorecards read 117-111, 117-111 and 118-110 in favour of the Valdez, thus retaining his WBO title. Quigg suffered a cut over his left eye in round 5 which caused him issues later in the fight whereas Valdez after having his mouth busted, was seen with blood pouring out in the second half of the fight. The difference in the fight was that Valdez had too much hand and foot speed for Quigg and was able unload on multiple punches on Quigg. Valdez's style of a higher punch output also caused him to take a lot of punishment throughout the fight. Valdez was hurt in round 5 from a big left hook from Quigg. In round 11, Valdez hurt Quigg with a hard head shot in the final 20 seconds. It was in round 11 that Quigg began to use his jab more to his own advantage. Valdez was then hurt by a low blow in that round. In round 12, Valdez tied Quigg up frequently and used movement to stay out of trouble. Quigg was humble in defeat stating the better man won, but felt it was closer. ESPN scored the fight for Valdez 115-113. They also reported that Quigg weighed 142.2 pounds compared to Valdez who was 135.6 pounds on fight night. CompuBox numbers showed that Valdez landed 238 of 914 punches thrown (26%), and Quigg landed 143 of his 595 thrown (24%). After the fight Quigg explained the reason he missed weight was because he had fractured his foot four weeks before the fight and unable to run to lose the extra pounds. Valdez visited oral surgeon Dr. Douglas Galen in Beverly Hills the following Monday and had his jaw wired shut. The card was watched by an average 1.1 million viewers on ESPN.


title: Óscar Valdez

text: On 13 August 2018 it was announced Valdez had left longtime trainer Manny Robles and would instead return to training under Eddy Reynoso, well known for training Saul "Canelo" Álvarez. One of the main reasons for the change was for Valdez to tighten his defence after being involved in slugfests since winning the WBO title. On 1 November, it was reported that Valdez was looking to make a return to the ring at the Mexico City Arena on 12 January 2019. Later that month, a fight against 33 year old Spanish boxer Andoni Gago (20-3-3, 6 KOs) was finalized and would take place in Tucson, Arizona. At the time, Gago was ranked #14 with the WBO, making it an official title defence. Entering the fight, Gago was unbeaten in five fights, having lost to Lee Selby in March 2017. In December, it was reported the card would be scrapped and Valdez's return would be postponed. The reason behind this was because Gago was unable to secure a travel visa in time to make the trip to the United States. Some sources stated Valdez would instead return on the Alvarez-Kovalev rematch undercard. A day later it was announced that Valdez would next fight at The Ford Center at The Star in Frisco, Texas on 2 February 2019, with Italian boxer Carmine Tommasone (19-0, 5 KOs) as his opponent.


title: Óscar Valdez

text: In his next fight, Valdez fought Jayson Velez. Valdez had a great fight, dropping Velez three times before ending the fight via TKO in the tenth round.


title: Óscar Valdez

text: On 20 February 2021, Valdez faced Miguel Berchelt for the WBC super featherweight title. The fight had originally been scheduled for 12 December 2020, however it was postponed after Berchelt tested positive for COVID-19. Despite entering the bout as the sizable betting underdog, Valdez won the bout via tenth-round knockout to become a two-division world champion.


title: Óscar Valdez

text: Valdez made his first defense of his WBC super featherweight title against the 2016 Olympic Gold medalist Robson Conceição on September 10, 2021, at the Casino Del Sol in Tucson, Arizona, United States. On August 31, it was revealed that Valdez had tested positive for the banned stimulant phentermine. On September 2, his B-sample tested positive as well. The fight with Conceição would still happen however, as the Pascua Yaqui Tribe Athletic Commission went by WADA guidelines, which only prohibit stimulants in-competition. Valdez won the closely contested fight by unanimous decision, with two judges awarding him a 115-112 scorecard, while the third judge scored it 117-110 for Valdez. Conceição had a better start to the fight, although he began to tire around the mid-rounds, after which Valdez began to take over. A number of fans and fighters disagreed with the scorecards, with Sunny Edwards stating "So you let him cheat with drugs, then gift him the scorecards", while Tony Harrison wrote "I don’t think Valdez won but that’s me on to the next". However, most media members scored the fight for Valdez.


title: Óscar Valdez

text: On January 16, 2022, rumors surfaced that Valdez would face the WBO junior lightweight champion Shakur Stevenson in a title unification bout on April 30, 2022, at the MGM Grand Garden Arena in Paradise, Nevada. Promoter Bob Arum revealed three days later that Valdez and Stevenson had come to terms to meet in a super-featherweight world title unification fight. The fight is expected to take place on April 30, at the MGM Grand Garden Arena in Paradise, Nevada. Valdez lost the fight by unanimous decision, with scores of 117–110, 118–109, and 118–109. The fight drew in an average of 1,353,000 viewers on ESPN and peaked at 1,440,000.


title: Óscar Valdez

text: On November 9, 2022, Valdez was ordered by the WBO to face the sanctioning body's reigning featherweight beltholder Emanuel Navarrete for the vacant WBO junior lightweight championship. The title bout was booked to take place on February 3rd, 2023, and headlined an ESPN broadcast card, which was expected to take place at the Desert Diamond Arena in Glendale, Arizona on February 3rd, 2023. Valdez withdrew from the fight on December 13, with an undisclosed injury. Navarrete was re-scheduled to face Liam Wilson, with the winner of the bout then expected to face Valdez.


title: Detroit Diesel

text: Detroit Diesel Corporation (DDC) is an American diesel engine manufacturer headquartered in Detroit, Michigan, United States. It is a subsidiary of Daimler Truck North America, which is itself a wholly owned subsidiary of the mulitinational Daimler Truck AG. The company manufactures heavy-duty engines and chassis components for the on-highway and vocational commercial truck markets. Detroit Diesel has built more than 5 million engines since 1938, more than 1 million of which are still in operation worldwide. Detroit Diesel's product line includes engines, axles, transmissions, and a Virtual Technician service.


title: Detroit Diesel

text: Detroit engines, transmissions, and axles are used in several models of truck manufactured by Daimler Truck North America.


title: Detroit Diesel

text: Detroit Diesel consists of manufacturing operations of axles, transmissions and diesel engines for on-highway only, which is owned by Daimler Truck AG. The former off-highway division was sold to MTU Friedrichshafen in 2006 and subsequently purchased by Rolls-Royce in 2014.


title: Detroit Diesel

text: In 1998, the EPA announced fines totaling $83.4 million against Detroit Diesel and six other diesel engine manufacturers, the largest fine to date, which evaded testing by shutting down emissions controls during highway driving while appearing to comply with lab testing. The manufacturers also agreed to spend more than $1 billion to correct the problem. The trucks used engine ECU software to engage pollution controls during the 20-minute lab tests to verify compliance with the Clean Air Act, but then disable the emissions controls during normal highway cruising, emitting up to three times the maximum allowed NOx pollution.


title: Detroit Diesel

text: In 2016, Detroit Diesel agreed to pay US$28.5 million to resolve violations of the US federal Clean Air Act. The company sold 7,786 heavy-duty diesel engines, which were assembled approximately 80% complete in 2009, including the crankshaft, block, pistons, and connecting rods, the short block engines were stored temporarily and completed the remaining assembly in early 2010 for use in trucks and buses of in model year 2010. These engines were alleged not to comply with stricter 2010 emission standards.


title: Extracurricular activity

text: An extracurricular activity (ECA) or extra academic activity (EAA) or cultural activities is an activity, performed by students, that falls outside the realm of the normal curriculum of school, college or university education. Such activities are generally voluntary (as opposed to mandatory), social, philanthropic, and often involve others of the same age. Students and staff direct these activities under faculty sponsorship, although student-led initiatives, such as independent newspapers, are very common. However, sometimes the school principals and teachers also bring in these activities in the school among the students.


title: Extracurricular activity

text: A group study conducted by surveying school-age students in the National Longitudinal Study of Adolescent Health revealed that 70% of adolescents in the USA are involved in some form of extracurricular activities.


title: Extracurricular activity

text: Other studies have shown being involved in extracurricular activities reduces the likelihood of dropping out of school, likelihood of committing a criminal offense, and leads to higher educational retainment and success and achievements in school work, not to mention that the greatest advantage of participating in at least one of these activities is the decrease in anti-social behaviors and students growing up to be more successful in communication and relationships.


title: Extracurricular activity

text: Involvement in after school clubs and extracurricular activities is beneficial in a variety of ways for the K-12 population. For example, school clubs can offer a place to form relationships and foster learning, and this was demonstrated with multiple groups. Research including students with disabilities involved in extracurricular activities show that they were more likely to have friends than those who were not involved. Similar findings with racial and ethnic minorities and immigrant adolescents showed that minority, first, and second generation adolescents were less likely than their counterparts to have friends and be engaged in relationships, however, extracurricular activities facilitated socialization. Thus, being involved in activities outside of school increases student’s chances of creating friendships. Also, extracurricular activities can provide families with a safe environment for their children while they are at work. This gives the parents an opportunity to get all the work time possible and allows the child to participate in educational or athletic activities. Furthermore, extracurricular activities increase positive self-development, regardless of where the activities take place (at school or away from school) Likewise, female adolescents involved in school based extracurricular activities had higher self-esteem than those not involved. The overall findings demonstrate that involvement in activities, whether it be sports, clubs, or school-based programs, have a positive impact on the participant’s life.


title: Extracurricular activity

text: Diversity in clubs and extracurricular activities plays an important role in adolescent lives and futures. Exposure to diverse groups can help promote adolescents to become socially intelligent and responsible adults. However, being immersed in diverse populations is not enough, as it is beneficial only if members engage with one another. More meaningful interactions with a diverse range of peers allows people to acquire traits such as more socially-responsible leadership skills. Furthermore, participating in ethnic clubs allowed minority groups to feel more connected to their cultures and allowed others to gain knowledge and understanding of other cultures. This has two key benefits: minority groups have a safe place to feel a sense of belonging to their cultural roots and background, and people of differing ethnic backgrounds have an opportunity to learn more about other cultures and thus become more culturally competent. Correlational studies showed positive relationships with involvement in ethnic/cultural clubs and intellectual and psychosocial development, multicultural competence, interpersonal skills, and leadership. Additionally, in school settings, interracial friendships positively impacted the individuals involved and the school culture as a whole. This demonstrates the importance of implementing multiculturalism into school environments, both academically and in extracurricular activities. It is important to continue research on incorporating multiculturalism and ethnic/cultural clubs into schools. Creating a multicultural competent environment for diverse student populations allows them to engage with others, discuss possible biases and stereotypes openly, and form meaningful intergroup relationships. If that is implemented at a young age, it is more likely to carry into adulthood, thus molding a more socially and culturally competent adult.


title: Extracurricular activity

text: An Extracurricular Management System (EMS) is a management information system for education establishments to manage extracurricular data and processes. The primary function of an EMS is to handle administrative tasks associated with the operation of an extracurricular program so that staff can focus on delivering great extracurricular activities and outcomes for students. Automating the basic administration tasks associated with extracurricular management saves educational institutions money and time, while also improving control and visibility. Extracurricular activities form an important part of the student experience, so managing them accurately and efficiently is of paramount importance in achieving positive outcomes for students.


title: Christianization of Scandinavia

text: The Christianization of Scandinavia, as well as other Nordic countries and the Baltic countries, took place between the 8th and the 12th centuries. The realms of Denmark, Norway and Sweden established their own Archdioceses, responsible directly to the Pope, in 1104, 1154 and 1164, respectively. The conversion to Christianity of the Scandinavian people required more time, since it took additional efforts to establish a network of churches.


title: Christianization of Scandinavia

text: The earliest signs of Christianization were in the 830s with Ansgar's construction of churches in Birka and Hedeby in the 830s. The conversion of Scandinavian kings occurred over the period 960–1020. Subsequently, Scandinavian kings sought to establish churches, dioceses and Christian kingship, as well as destroy pagan temples. Denmark was the first Scandinavian country to Christianize, as Harald Bluetooth declared this around AD 975, and raised the larger of the two Jelling Stones. According to historian Anders Winroth, Christianity was not forced upon Scandinavians by foreign states or foreign missionaries, but instead willfully adopted by Scandinavian kings who saw the religion as politically advantageous.


title: Christianization of Scandinavia

text: Although the Scandinavians became nominally Christian, it took considerably longer for actual Christian beliefs to establish themselves among the people in some regions, while the people were Christianized before the king in other regions. During the Early Middle Ages the papacy had not yet manifested itself as the central Roman Catholic authority, thus making it possible for regional variants of Christianity to develop.


title: Christianization of Scandinavia

text: Recorded missionary efforts in Denmark started with Willibrord, "Apostle to the Frisians", who preached in Schleswig, which at the time was part of Denmark. He went north from Frisia sometime between 710 and 718 during the reign of King Ongendus. Willibrord and his companions had little success: the king was respectful but had no interest in changing his beliefs. Agantyr did permit 30 young men to return to Frisia with Willibrord. Perhaps Willibrord's intent was to educate them and recruit some of them to join his efforts to bring Christianity to the Danes. A century later Ebbo, Archbishop of Reims and Willerich, later Bishop of Bremen, baptized a few persons during their 823 visit to Denmark. He returned to Denmark twice to proselytize but without any recorded success.


title: Christianization of Scandinavia

text: In 826, the King of Jutland Harald Klak was forced to flee from Denmark by Horik I, Denmark's other king. Harald went to Emperor Louis I of Germany to seek help getting his lands in Jutland back. Louis I offered to make Harald Duke of Frisia if he would give up the old gods. Harald agreed, and his family and the 400 Danes with him were baptized in Ingelheim am Rhein. When Harald returned to Jutland, Emperor Louis and Ebbo of Rheims assigned the monk Ansgar to accompany Harald and oversee Christianity among the converts. When Harald Klak was forced from Denmark by King Horik I again, Ansgar left Denmark and focused his efforts on the Swedes. Ansgar traveled to Birka in 829 and established a small Christian community there. His most important convert was Herigar, described as a prefect of the town and a counselor to the king. In 831 the Archdiocese of Hamburg was founded and assigned responsibility for proselytizing Scandinavia.


title: Christianization of Scandinavia

text: Horik I sacked Hamburg in 845 where Ansgar had become the archbishop. The seat of the archdiocese was transferred to Bremen. In the same year there was a pagan uprising in Birka that resulted in the martyrdom of Nithard and forced the resident missionary Bishop Gautbert to flee. Ansgar returned to Birka in 854 and Denmark in 860 to reestablish some of the gains of his first visits. In Denmark he won over the trust of then-King Horik II (not Horik I, who was murdered in 854 and opposed Christianity) who gave him land in Hedeby (proto-town to be replaced by Schleswig) for the first Christian chapel. A second church was founded a few years later in Ribe on Denmark's west coast. Ribe was an important trading town, and as a result, southern Denmark was made a diocese in 948 with Ribe as its seat, a part of the Archdiocese of Hamburg-Bremen under its first bishop, St. Leofdag who was murdered that year while crossing the Ribe River.


title: Christianization of Scandinavia

text: The supremacy of the archdiocese of Hamburg-Bremen over ecclesiastical life in the north gradually declined as the papacy, from the pontificate of Pope Gregory VII onwards, involved itself more with the North directly. A significant step in this direction was the foundation of an archbishopric for the whole of Scandinavia at Lund in 1103–04.


title: Christianization of Scandinavia

text: Both the accounts of Willibrod and of Harald are semi-mythical, and integrate mythical and legendary themes from the Nordic pagan tradition into their Christian stories. A syncretized variant of the story of Harald, that has him battling Ragnar Lodbrok to establish Christianity in Denmark, appears in Book Nine of Saxo Grammaticus' Gesta Danorum. Ebbo is the name of a mythical Nordic figure, Ibor, also known as Egil or Orvandil, who is an archer, elf, and smith who turns against the Aesir gods and wages war upon them, and the story of Ebbo of Rheims integrates themes of the divine Ebbo's story, including peasant (non-Aesir) birth and migration. Harald's usurpation and his efforts at Christianization are related to several stories of "usurpation" and "changes in sacrifices", including the usurpation of Mithothyn and the introduction of the worship of Frey at Uppsala, in that they utilize similar motifs and mythical figures.


title: Christianization of Scandinavia

text: The spread of Christianity in Denmark occurred intermittently. Danes encountered Christians when they participated in Viking raids from the 9th century to the 1060s. Danes were still tribal in the sense that local chiefs determined attitudes towards Christianity and Christians for their clan and kinsmen. Bringing Christian slaves or future wives back from a Viking raid brought large numbers of ordinary Danes into close contact with Christians for perhaps the first time.


title: Christianization of Scandinavia

text: As the chiefs and kings of Denmark became involved in the politics of Normandy, England, Ireland, France, and Germany, they adopted a kinder attitude toward their Christian subjects. In some cases the conversion of the chief or king appears to be purely political to assure an alliance or prevent powerful Christian neighbours from attacking. There were instances when the conversion of a powerful chief (Danish: "jarl") or one of the kings was followed by wholesale conversions among their followers. In a few instances conversion was brought about by trial by ordeal miracles wrought by saintly Christians in the presence of the king or other great men of the time.


title: Christianization of Scandinavia

text: Christian missionaries recognized early on that the Danes did not worship stone or wooden idols as the north Germans or some Swedes did. They could not simply destroy an image to prove that Christ was a superior god. The great religious sites at Viborg, Lejre, Lund, and Odense were also the location of Denmark's great assembly places (Danish: "landsting"). Religious sites in Denmark were often located at sacred springs, magnificent beech groves, or isolated hilltops. Missionaries simply asked to build chapels in those places. Over time the religious significance of the place transferred itself to the chapel.


title: Christianization of Scandinavia

text: Even after becoming Christian, Danes blended the two belief systems together. Families who lived close to the earth did not want to offend the local spirits (Danish: "landvætter"), so offerings were left just as they had been in pre-Christian times. Sacred springs (Danish: "kilder") were simply consecrated to one of the local saints associated with the spring and life went on much as it had before. Christian missionaries were able to help the process along by locating churches on or near sacred places, in some cases actually using wood from the sacred groves for church construction. Thor's hammer sign was easily absorbed by the cross.


title: Christianization of Scandinavia

text: Denmark has several saints, canonized by local bishops as was the custom in early Scandinavia or revered by locals as saints. Often these saints derive their veneration from deeds associated with the Christianization of Denmark. Viborg has St Kjeld, Aarhus has St Niels (also called St Nickolas), Odense has St Canute (Danish: "Sanct Knud"). Others include Canute Lavard, Ansgar, of Vendsyssel, St Wilhelm, St Leofdag of Ribe, and others gave their lives and efforts to the task of making the Danes Christian.


title: Christianization of Scandinavia

text: King Gorm the Old (Danish: "den Gamle"), who was known in his lifetime as Gorm the Sleepy, was the first king of all of Denmark. Until his day, Danish kings were presumably local kings without influence over all the Danes. Denmark consisted of Jutland and Schleswig and Holstein all the way down to the Eider River, the main islands of Zealand, Funen, Langeland, the nearby lesser islands, and Skåneland. Gorm was said to be "hard and heathen", but Queen Thyra's influence permitted Christians to live more or less without trouble. The double barrow of Gorm and Thyra at Jelling contained a mixture of pagan and Christian iconography, including a decorated silver cup. Gorm and Queen Thyra's son, King Harald Bluetooth, boasted on one of the stones at Jelling that he had "made the Danes Christian". Harald Bluetooth is also mentioned in the inscription on the Curmsun Disc, dated AD 960s–980s. On the reverse of the disc there is an octagonal ridge, which runs around the edge of the object. In the center of the octagonal ridge there is a Latin cross which may indicate that Harald Bluetooth was Christian.


title: Christianization of Scandinavia

text: The first Danish king to convert to Christianity was Harald Klak, who had himself baptised during his exile in order to receive the support of Louis the Pious. Rimbert reports that he set out to return home, accompanied by missionaries; however, Sanmark regards it as "unlikely" that he actually returned home and thus considers his impact on the conversion of Denmark as "probably minor."


title: Christianization of Scandinavia

text: Christianity only gained a strong hold in Denmark following the baptism of Harald Bluetooth. Initially, Harald had remained pagan, although he had allowed public preaching by Christian missionaries as early as 935. Around 960, Bluetooth converted to Christianity, reportedly when the Frisian monk Poppo held a fire-heated lump of iron in his hand without injury. Harald's daughter, Gunhilde, and his son, Sweyn Forkbeard were baptized, too. There was also a political reason for conversion. German histories record Harald being baptized in the presence of Emperor Otto I, Sweyn Forkbeard's godfather. One consequence of his conversion is that Danish kings abandoned the old royal enclosure at Jelling and moved their residence to Roskilde on the island of Zealand.


title: Christianization of Scandinavia

text: Sweyn rebelled against his father, who spent an inordinate amount of time and money raising a great stone at Jelling to commemorate his accomplishments. One day King Harald asked a traveller if he had ever seen human beings move such a heavy load. "I have seen Sweyn drag all of Denmark away from you, sir. Judge for yourself which of you bears the heavier weight." Harald left the stone lying in the path, realizing at last that Sweyn had nearly succeeded in stealing the whole kingdom. Several battles brought the rebellion to stalemate, but in 985 Harald was mortally wounded by an arrow. Later his remains were buried in the little timber church at Roskilde, then Denmark's capital. His remains are supposed to be walled up in one of the pillars of Roskilde Cathedral.


title: Christianization of Scandinavia

text: Sweyn Forkbeard tried to wrest control of the church in Denmark away from the Holy Roman Empire and as a result was slandered by German historians of his day. He has been accused of relapsing from his Christian beliefs and persecuting Christians in England. In fact Sweyn gave land to the large cathedral at Lund to pay for the maintenance of the chapter. His army destroyed Christian churches in England as part of his invasion following the St. Brice's Day massacre of Danes organized by Aethelred. But when Sweyn became King of England and of Denmark, politics required that he show a kinder face toward the church which had opposed him.


title: Christianization of Scandinavia

text: Another Christianizing influence was the mass emigration of Danes to England and Normandy in the Viking years. Thousands of Danes settled in east central England and in northern France displacing or intermarrying with the locals who were Christian. Once part of a Danish clan became Christian, it often meant that the rest of the family's view toward Christianity softened.


title: Christianization of Scandinavia

text: By the early 11th century, certainly during the reign of Canute IV, Denmark can be said to be a Christian country. Later known as St. Canute, Canute IV was murdered inside St. Albans Church in 1086 after nobles and peasants alike rebelled at his enforcing the tithe to pay for the new monasteries and other ecclesiastical foundations which were introduced into Denmark for the first time during his reign. Both the institutions and the tax were considered foreign influences, and Canute's refusal to use the regional assemblies as was customary to establish new laws, resulted in his death and that of his brother, Prince Benedict, and seventeen other housecarls. In many ways the canonization of St. Canute in 1188 marks the triumph of Christianity in Denmark. When St. Canute's remains were moved into Odense Cathedral, the entire nation humbled itself with a three-day fast. Although he was not the first Dane to be made a saint, it was the first time for a king, the symbol of a more or less united Denmark, was recognized as an example worthy of veneration by the faithful.


title: Christianization of Scandinavia

text: From that time until 1536 when Denmark became a Lutheran country under the King (or Queen) of Denmark as the titular head of the Danish National Church, (Danish: "Folkekirke") the struggle between the power of the king and nobles and the church would define much of the course of Danish history.


title: Christianization of Scandinavia

text: The first recorded attempts at spreading Christianity in Norway were made by King Haakon the Good in the tenth century, who was raised in England. His efforts were unpopular and were met with little success. The subsequent King Harald Greyhide, also a Christian, was known for destroying pagan temples but not for efforts to popularize Christianity.


title: Christianization of Scandinavia

text: He was followed by the staunchly pagan Haakon Sigurdsson Jarl, who led a revival of paganism with the rebuilding of temples. When Harold I of Denmark attempted to force Christianity upon him around 975, Haakon broke his allegiance to Denmark. A Danish invasion force was defeated at the battle of Hjörungavágr in 986.


title: Christianization of Scandinavia

text: In 995 Olaf Tryggvason became King Olaf I of Norway. Olaf had raided various European cities and fought in several wars. In 986, however, he (supposedly) met a Christian seer on the Isles of Scilly. As the seer foretold, Olaf was attacked by a group of mutineers upon returning to his ships. As soon as he had recovered from his wounds, he let himself be baptized. He then stopped raiding Christian cities and lived in England and Ireland. In 995 he used an opportunity to return to Norway. When he arrived, Haakon Jarl was already facing a revolt, and Olaf Tryggvason could convince the rebels to accept him as their king. Haakon Jarl was later betrayed and killed by his own slave, while he was hiding from the rebels in a pig sty.


title: Christianization of Scandinavia

text: Olaf I then made it his priority to convert the country to Christianity using all means at his disposal. Expanding his efforts to the Norse settlements in the west the kings' sagas credit him with Christianizing the Faroes, Orkney, Shetland, Iceland, and Greenland.


title: Christianization of Scandinavia

text: After Olaf's defeat at the Battle of Svolder in 1000 there was a partial return to paganism in Norway under the rule of the Jarls of Lade. In the following reign of Saint Olaf, pagan remnants were stamped out and Christianity entrenched.


title: Christianization of Scandinavia

text: Nicholas Breakspear, later Pope Adrian IV, visited Norway from 1152 to 1154. During his visit, he set out a church structure for Norway. The Papal bull confirming the establishment of a Norwegian archdiocese at Nidaros is dated 30 November 1154.


title: Christianization of Scandinavia

text: Thirteenth-century runic inscriptions from the merchant town of Bergen in Norway show little Christian influence, and one of them appeals to a Valkyrie.


title: Christianization of Scandinavia

text: The first known attempts to Christianize Sweden were made by Ansgar in 830, invited by the Swedish king Björn. Setting up a church at Birka he met with little Swedish interest. A century later Unni, archbishop of Hamburg, made another unsuccessful attempt. In the 10th century English missionaries made inroads in Västergötland.


title: Christianization of Scandinavia

text: Newer archaeological research suggests there were Christians in Götaland already during the 9th century; it is further believed Christianity came from the southwest and moved towards the north.


title: Christianization of Scandinavia

text: The supporters of the cult at Uppsala drew a mutual agreement of toleration with Olof Skötkonung, the first Christian king of Sweden, who ascended to the throne in the 990s. Presumably Olof Skötkonung was not in a powerful enough position to violently enforce the observance of Christianity in Uppland. Instead he established an episcopal see at Skara in Västergötland, near his own stronghold at Husaby around 1000. Another episcopal see was established at Sigtuna in the 1060s by King Stenkil, according to Adam of Bremen. This seat was moved to Gamla Uppsala probably some time between 1134 and 1140. This might have been because of Uppsala's importance as an old royal residence and thing site, but it may also have been inspired by a desire to show that the resistance to Christianity in Uppland had been defeated. By papal initiative an archdiocese for Sweden was established at Uppsala in 1164.


title: Christianization of Scandinavia

text: What may be one of the most violent occurrences between Christians and pagans was a conflict between Blot-Sweyn and Inge the Elder in the 1080s. This account survives in the "Orkneyinga saga" and in the last chapter of "Hervarar saga" where the saga successively moves from legendary history to historic Swedish events during the centuries before its compilation. The reigning king Inge decided to end the traditional pagan sacrifices at Uppsala which caused a public counter-reaction. Inge was forced into exile, and his brother-in-law Blot-Sweyn was elected king on condition that he allow the sacrifices to continue. After three years in exile, Inge returned secretly to Sweden in 1087, and having arrived at Old Uppsala, he surrounded the hall of Blot-Sweyn with his húskarls and set the hall on fire, slaying the king as he escaped from the burning house. "Hervarar saga" reports that Inge completed the Christianization of the Swedes, but the "Heimskringla" suggests that Inge could not assume power directly, but had to dispose of yet another pagan king, Eric of Good Harvests.


title: Christianization of Scandinavia

text: According to M. G. Larsson, the reason why the Swedish core provinces had coexistence between paganism and Christianity throughout the 11th century was because there was a general support for the transition towards the new religion. However, the old pagan rites were important and central for legal processes and when someone questioned ancient practices, many newly Christianized Swedes could react strongly in support of paganism for a while. Larsson theorizes that, consequently, the vacillation between paganism and Christianity that is reported by the sagas and by Adam of Bremen was not very different from vacillations that appear in modern ideological shifts. It would have been impossible for King Inge the Elder to rule as a Christian king without strong support from his subjects, and a Norwegian invasion of Västergötland by Magnus Barefoot put Inge's relationship with his subjects to the test: he appears to have mustered most of the Swedish leidang, 3,600 men, and he ousted the Norwegian occupation force.


title: Christianization of Scandinavia

text: Although Sweden was officially Christianized by the 12th century, the Norwegian king Sigurd the Crusader undertook a crusade against Småland, the south-eastern part of the Swedish kingdom, in the early 12th century, and officially it was in order to convert the locals.


title: Christianization of Scandinavia

text: Archaeological excavations of burial sites on the island of Lovön near modern-day Stockholm have shown that the actual Christianization of the people was very slow and took at least 150 to 200 years.


title: Christianization of Scandinavia

text: On the Swedish island of Gotland a Gotlandic law book known as the Gutalagen was officially in use from the 1220s until 1595. Still, in practice it remained in use until 1645. This law book stated that the performance of blóts was punishable by a fine.


title: Christianization of Scandinavia

text: On the northernmost runestone of the world standing on the island Frösön in central Jämtland, the Frösö Runestone, it is said that a man called Austmaðr Christianized the region, probably in the period 1030–1050 when the runestone was raised. Little is known of Austmaðr, but he is believed to have been the lawspeaker of the regional thing Jamtamót.


title: Christianization of Scandinavia

text: The Scandinavian medieval kings also ruled over provinces outside of Scandinavia. These provinces are today known as the Nordic countries.


title: Christianization of Scandinavia

text: Sigmundur Brestisson was the first Faroe-man to convert to the Christian faith, bringing Christianity to the Faroes at the decree of Olaf Tryggvason. Initially Sigmundur sought to convert the islanders by reading the decree to the Alting in Tórshavn but was nearly killed by the resulting angry mob. He then changed his tactics, went with armed men to the residence of the chieftain Tróndur í Gøtu and broke in his house by night. He offered him the choice between accepting Christianity or face beheading; he chose the former.


title: Christianization of Scandinavia

text: Later on, in 1005, Tróndur í Gøtu attacked Sigmundur by night at his yard in Skúvoy, whereupon Sigmundur fled by swimming to Sandvík on Suðuroy. He reached land in Sigmundargjógv in Sandvík, but a farmer in the village killed the exhausted Sigmundur and stole his precious golden arm ring.


title: Christianization of Scandinavia

text: Judging by archaeological finds, Christianity gained a foothold in Finland during the 11th century. The Catholic church was strengthened with growing Swedish influence in the 12th century and the Finnish "crusade" of Birger Jarl in the 13th century. Finland was part of Sweden since then until the 19th century.


title: Christianization of Scandinavia

text: Irish monks known as Papar are said to have been present in Iceland before its settlement by the Norse in the 9th century.


title: Christianization of Scandinavia

text: Following King Olaf I's taking of Icelandic hostages, there was tension between the Christian and pagan factions in 10th century Iceland. Violent clashes were avoided by the decision of the Althing in 1000 AD to put the arbitration between them to Þorgeir Ljósvetningagoði, the leader of the pagan faction. He opted, after a day and a night of meditation, that the country should convert to Christianity as a whole, while pagan worship in private would continue to be tolerated.


title: Christianization of Scandinavia

text: Some conversions appear to have taken place for political and material gain, while others were for spiritual reasons. For instance, some may have simply wanted to take the rich gifts (such as a fine, white baptismal garment) that were being handed out by Frankish nobles, who acted as the baptismal candidates' sponsors, when they were baptized. In the case of King Harald Bluetooth of Denmark, for example, he only partially converted to the new faith (at least at first) to preserve his independence from the Germans, who posed an even greater threat at the time than the Franks had been prior to this. He also saw that Christianity had much to offer to his rule. It not only helped to exalt his status, but it also provided practical help. The Missionary bishops were literate, and those who had experience of the royal government in Germany or England had the potential to be valuable advisors. There was also an economic motive to convert as pagan kings were fascinated with Christian wealth. As a result, some chose to accept the new faith as a way to gain access to this wealth.


title: Christianization of Scandinavia

text: In 1721, a new Danish-Norwegian colony was started in Greenland with the objective of converting the inhabitants to Christianity. Around the same time efforts were made in Norway and Sweden to convert the Sami, who had remained pagan long after the conversion of their neighbours. Some Sami remained unconverted until the 18th century.


title: Christianization of Scandinavia

text: Research shows that Scandinavian countries such as Denmark and Sweden are currently among the least religious nations in the world; nevertheless, "many Danes and Swedes, for instance, will profess belief in 'something,' although not necessarily the God of the Bible." Phil Zuckerman writes in a 2009 article to the "Nordic Journal of Religion and Society," "Surely the historical developments of culture and religion in Denmark and Sweden are crucially informing factors in explaining the current state of irreligiosity."


title: Glovo

text: Glovo is a Spanish quick-commerce start-up founded in Barcelona, Spain, in 2015 by Oscar Pierre and Sacha Michaud. It is an on-demand courier service that purchases, picks up, and delivers products ordered through its mobile app. It offers multiple services with food delivery being the most popular.


title: Glovo

text: Founded by Oscar Pierre (CEO) and co-founder Sacha Michaud, Glovo's first meetings were in a McDonald's. It eventually expanded into other countries, but, in January 2020, Glovo ended its operations in Turkey, Egypt, Puerto Rico and Uruguay.


title: Glovo

text: In October 2020, in an effort to achieve profitability, Glovo's remaining Latin American operations were purchased by Delivery Hero (DH), a German company, in a deal worth US$272 million, leaving Glovo with just its Southern and Eastern Europe operations. In September 2022, Glovo was fined $78 million for labor breaches in Spain.


title: Glovo

text: In December 2021, DH signed a deal to become Glovo's majority shareholder, acquiring an additional 39.4% stake of the Spanish delivery company. The acquisition was completed in July 2022 and since then it has owned a majority stake in Glovo (94%).


title: Glovo

text: Food delivery service is the company's most popular service. Other services available include pharmacy, courier and quiero (anything).


title: Glovo

text: The food business allows users to find and place orders with their favourite restaurants which is picked up when ready and delivered to the user's doorstep. While this model continues to be its flagship service, the company is reported experimenting with CloudKitchens and Grocery Darkstores.


title: Group action

text: In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group "acts" on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it. For example, it acts on the set of all triangles. Similarly, the group of symmetries of a polyhedron acts on the vertices, the edges, and the faces of the polyhedron.


title: Group action

text: A group action on a vector space is called a representation of the group. In the case of a finite-dimensional vector space, it allows one to identify many groups with subgroups of , the group of the invertible matrices of dimension over a field .


title: Group action

text: The symmetric group acts on any set with elements by permuting the elements of the set. Although the group of all permutations of a set depends formally on the set, the concept of group action allows one to consider a single group for studying the permutations of all sets with the same cardinality.


title: Group action

text: If is a group with identity element , and is a set, then a ("left") "group action" of on is a function


title: Group action

text: The group is said to act on (from the left). A set together with an action of is called a ("left") -"set".


title: Group action

text: From these two axioms, it follows that for any fixed in , the function from to itself which maps to is a bijection, with inverse bijection the corresponding map for . Therefore, one may equivalently define a group action of on as a group homomorphism from into the symmetric group of all bijections from to itself.


title: Group action

text: The difference between left and right actions is in the order in which a product acts on . For a left action, acts first, followed by second. For a right action, acts first, followed by second. Because of the formula , a left action can be constructed from a right action by composing with the inverse operation of the group. Also, a right action of a group on can be considered as a left action of its opposite group on .


title: Group action

text: Thus, for establishing general properties of group actions, it suffices to consider only left actions. However, there are cases where this is not possible. For example, the multiplication of a group induces both a left action and a right action on the group itself—multiplication on the left and on the right, respectively.


title: Group action

text: Let formula_3 be a group acting on a set formula_4. The action is called ' or ' if formula_5 for all formula_6 implies that formula_7. Equivalently, the morphism from formula_3 to the group of bijections of formula_4 corresponding to the action is injective.


title: Group action

text: The action is called "" (or "semiregular" or "fixed-point free") if the statement that formula_5 for some formula_6 already implies that formula_7. In other words, no non-trivial element of formula_3 fixes a point of formula_4. This is a much stronger property than faithfulness.


title: Group action

text: For example, the action of any group on itself by left multiplication is free. This observation implies Cayley's theorem that any group can be embedded in a symmetric group (which is infinite when the group is). A finite group may act faithfully on a set of size much smaller than its cardinality (however such an action cannot be free). For instance the abelian 2-group formula_15 (of cardinality formula_16) acts faithfully on a set of size formula_17. This is not always the case, for example the cyclic group formula_18 cannot act faithfully on a set of size less than formula_16.


title: Group action

text: In general the smallest set on which a faithful action can be defined can vary greatly for groups of the same size. For example, three groups of size 120 are the symmetric group formula_20, the icosahedral group formula_21 and the cyclic group formula_22. The smallest sets on which faithful actions can be defined for these groups are of size 5, 12, and 16 respectively.


title: Group action

text: The action of formula_3 on formula_4 is called "" if for any two points formula_25 there exists a formula_26 so that formula_27.


title: Group action

text: The action is ' (or "sharply transitive", or ') if it is both transitive and free. This means that given formula_25 the element formula_29 in the definition of transitivity is unique. If formula_4 is acted upon simply transitively by a group formula_3 then it is called a principal homogeneous space for formula_3 or a formula_3-torsor.


title: Group action

text: For an integer formula_34, the action is if formula_4 has at least formula_36 elements, and for any pair of formula_36-tuples formula_38 with pairwise distinct entries (that is formula_39, formula_40 when formula_41) there exists a formula_26 such that formula_43 for formula_44. In other words the action on the subset of formula_45 of tuples without repeated entries is transitive. For formula_46 this is often called double, respectively triple, transitivity. The class of 2-transitive groups (that is, subgroups of a finite symmetric group whose action is 2-transitive) and more generally multiply transitive groups is well-studied in finite group theory.


title: Group action

text: The action of the symmetric group of formula_4 is transitive, in fact formula_36-transitive for any formula_36 up to the cardinality of formula_4. If formula_4 has cardinality formula_53 the action of the alternating group is formula_54-transitive but not formula_55-transitive.


title: Group action

text: The action of the general linear group of a vector space formula_56 on the set formula_57 of non-zero vectors is transitive, but not 2-transitive (similarly for the action of the special linear group if the dimension of formula_58 is at least 2). The action of the orthogonal group of a Euclidean space is not transitive on nonzero vectors but it is on the unit sphere.


title: Group action

text: The action of formula_3 on formula_4 is called "primitive" if there is no partition of formula_4 preserved by all elements of formula_3 apart from the trivial partitions (the partition in a single piece and its dual, the partition into singletons).


title: Group action

text: The action is "wandering" if every formula_6 has a neighbourhood formula_66 such that there are only finitely many formula_26 with formula_68.


title: Group action

text: More generally, a point formula_6 is called a point of discontinuity for the action of formula_3 if there is an open subset formula_71 such that there are only finitely many formula_26 with formula_68. The "domain of discontinuity" of the action is the set of all points of discontinuity. Equivalently it is the largest formula_3-stable open subset formula_75 such that the action of formula_3 on formula_77 is wandering. In a dynamical context this is also called "wandering set".


title: Group action

text: The action is "properly discontinuous" if for every compact subset formula_78 there are finitely many formula_26 such that formula_80. This is strictly stronger than wandering; for instance the action of formula_81 on formula_82 given by formula_83 is wandering and free but not properly discontinuous.


title: Group action

text: The action by deck transformations of the fundamental group of a locally simply connected space on an covering space is wandering and free. Such actions can be characterized by the following property: every formula_6 has a neighbourhood formula_66 such that formula_86 for every formula_87. Actions with this property are sometimes called "freely discontinuous", and the largest subset on which the action is freely discontinuous is then called the "free regular set".


title: Group action

text: An action of a group formula_3 on a locally compact space formula_4 is called "cocompact" if there exists a compact subset formula_90 such that formula_91. For a properly discontinuous action, cocompactness is equivalent to compactness of the quotient space formula_92.


title: Group action

text: Now assume formula_3 is a topological group and formula_4 a topological space on which it acts by homeomorphisms. The action is said to be "continuous" if the map formula_95 is continuous for the product topology.


title: Group action

text: The action is said to be "" if the map formula_96 defined by formula_97 is proper. This means that given compact sets formula_98 the set of formula_26 such that formula_100 is compact. In particular, this is equivalent to proper discontinuity when formula_3 is a discrete group.


title: Group action

text: It is said to be "locally free" if there exists a neighbourhood formula_66 of formula_103 such that formula_104 for all formula_6 and formula_106.


title: Group action

text: The action is said to be "strongly continuous" if the orbital map formula_107 is continuous for every formula_108. Contrary to what the name suggests, this is a weaker property than continuity of the action.


title: Group action

text: If formula_3 is a Lie group and formula_4 a differentiable manifold, then the subspace of "smooth points" for the action is the set of points formula_6 such that the map formula_112 is smooth. There is a well-developed theory of Lie group actions, i.e. action which are smooth on the whole space.


title: Group action

text: If formula_29 acts by linear transformations on a module over a commutative ring, the action is said to be irreducible if there are no proper nonzero formula_29-invariant submodules. It is said to be "semisimple" if it decomposes as a direct sum of irreducible actions.


title: Group action

text: Consider a group "G" acting on a set "X". The "" of an element "x" in "X" is the set of elements in "X" to which "x" can be moved by the elements of "G". The orbit of "x" is denoted by formula_115:


title: Group action

text: The defining properties of a group guarantee that the set of orbits of (points "x" in) "X" under the action of "G" form a partition of "X". The associated equivalence relation is defined by saying formula_117 if and only if there exists a "g" in "G" with formula_118 The orbits are then the equivalence classes under this relation; two elements "x" and "y" are equivalent if and only if their orbits are the same, that is, formula_119


title: Group action

text: The group action is transitive if and only if it has exactly one orbit, that is, if there exists "x" in "X" with formula_120 This is the case if and only if formula_121 for "x" in "X" (given that "X" is non-empty).


title: Group action

text: The set of all orbits of "X" under the action of "G" is written as "X"/"G" (or, less frequently: "G"\"X"), and is called the ' of the action. In geometric situations it may be called the ', while in algebraic situations it may be called the space of "", and written formula_122 by contrast with the invariants (fixed points), denoted "X": the coinvariants are a while the invariants are a . The coinvariant terminology and notation are used particularly in group cohomology and group homology, which use the same superscript/subscript convention.


title: Group action

text: If "Y" is a subset of "X", then formula_123 denotes the set formula_124 The subset "Y" is said to be "invariant under G" if formula_125 (which is equivalent to formula_126). In that case, "G" also operates on "Y" by restricting the action to "Y". The subset "Y" is called "fixed under G" if formula_127 for all "g" in "G" and all "y" in "Y". Every subset that is fixed under "G" is also invariant under "G", but not conversely.


title: Group action

text: Every orbit is an invariant subset of "X" on which "G" acts transitively. Conversely, any invariant subset of "X" is a union of orbits. The action of "G" on "X" is "transitive" if and only if all elements are equivalent, meaning that there is only one orbit.


title: Group action

text: A "G-invariant" element of "X" is formula_6 such that formula_5 for all formula_130 The set of all such "x" is denoted formula_131 and called the "G-invariants" of "X". When "X" is a "G"-module, "X" is the zeroth cohomology group of "G" with coefficients in "X", and the higher cohomology groups are the derived functors of the functor of "G"-invariants.


title: Group action

text: Given "g" in "G" and "x" in "X" with formula_132 it is said that ""x" is a fixed point of "g"" or that ""g" fixes "x"". For every "x" in "X", the of "G" with respect to "x" (also called the "isotropy group" or "little group") is the set of all elements in "G" that fix "x":


title: Group action

text: This is a subgroup of "G", though typically not a normal one. The action of "G" on "X" is free if and only if all stabilizers are trivial. The kernel "N" of the homomorphism with the symmetric group, formula_134 is given by the intersection of the stabilizers "G" for all "x" in "X". If "N" is trivial, the action is said to be faithful (or effective).


title: Group action

text: Let "x" and "y" be two elements in "X", and let formula_29 be a group element such that formula_136 Then the two stabilizer groups formula_137 and formula_138 are related by formula_139 Proof: by definition, formula_140 if and only if formula_141 Applying formula_142 to both sides of this equality yields formula_143 that is, formula_144 An opposite inclusion follows similarly by taking formula_145 and supposing formula_146


title: Group action

text: The above says that the stabilizers of elements in the same orbit are conjugate to each other. Thus, to each orbit, we can associate a conjugacy class of a subgroup of "G" (that is, the set of all conjugates of the subgroup). Let formula_147 denote the conjugacy class of "H". Then the orbit "O" has type formula_147 if the stabilizer formula_137 of some/any "x" in "O" belongs to formula_147. A maximal orbit type is often called a principal orbit type.


title: Group action

text: Orbits and stabilizers are closely related. For a fixed "x" in "X", consider the map formula_151 given by formula_152 By definition the image formula_153 of this map is the orbit formula_154 The condition for two elements to have the same image is


title: Group action

text: In other words, formula_156 "if and only if" formula_29 and formula_158 lie in the same coset for the stabilizer subgroup formula_137. Thus, the fiber formula_160 of "f" over any "y" in "G"·"x" is contained in such a coset, and every such coset also occurs as a fiber. Therefore "f" induces a between the set formula_161 of cosets for the stabilizer subgroup and the orbit formula_162 which sends formula_163. This result is known as the "orbit-stabilizer theorem".


title: Group action

text: in other words the length of the orbit of "x" times the order of its stabilizer is the order of the group. In particular that implies that the orbit length is a divisor of the group order.


title: Group action

text: This result is especially useful since it can be employed for counting arguments (typically in situations where "X" is finite as well).


title: Group action

text: where "X" is the set of points fixed by "g". This result is mainly of use when "G" and "X" are finite, when it can be interpreted as follows: the number of orbits is equal to the average number of points fixed per group element.


title: Group action

text: Fixing a group "G", the set of formal differences of finite "G"-sets forms a ring called the Burnside ring of "G", where addition corresponds to disjoint union, and multiplication to Cartesian product.


title: Group action

text: The notion of group action can be encoded by the "action groupoid" formula_183 associated to the group action. The stabilizers of the action are the vertex groups of the groupoid and the orbits of the action are its components.


title: Group action

text: If "X" and "Y" are two "G"-sets, a "morphism" from "X" to "Y" is a function such that for all "g" in "G" and all "x" in "X". Morphisms of "G"-sets are also called "equivariant maps" or "G-maps".


title: Group action

text: The composition of two morphisms is again a morphism. If a morphism "f" is bijective, then its inverse is also a morphism. In this case "f" is called an "isomorphism", and the two "G"-sets "X" and "Y" are called "isomorphic"; for all practical purposes, isomorphic "G"-sets are indistinguishable.


title: Group action

text: With this notion of morphism, the collection of all "G"-sets forms a category; this category is a Grothendieck topos (in fact, assuming a classical metalogic, this topos will even be Boolean).


title: Group action

text: We can also consider actions of monoids on sets, by using the same two axioms as above. This does not define bijective maps and equivalence relations however. See semigroup action.


title: Group action

text: Instead of actions on sets, we can define actions of groups and monoids on objects of an arbitrary category: start with an object "X" of some category, and then define an action on "X" as a monoid homomorphism into the monoid of endomorphisms of "X". If "X" has an underlying set, then all definitions and facts stated above can be carried over. For example, if we take the category of vector spaces, we obtain group representations in this fashion.


title: Group action

text: We can view a group "G" as a category with a single object in which every morphism is invertible. A (left) group action is then nothing but a (covariant) functor from "G" to the category of sets, and a group representation is a functor from "G" to the category of vector spaces. A morphism between G-sets is then a natural transformation between the group action functors. In analogy, an action of a groupoid is a functor from the groupoid to the category of sets or to some other category.


title: Group action

text: In addition to continuous actions of topological groups on topological spaces, one also often considers smooth actions of Lie groups on smooth manifolds, regular actions of algebraic groups on algebraic varieties, and actions of group schemes on schemes. All of these are examples of group objects acting on objects of their respective category.


title: Gathering Blue

text: Gathering Blue is a young adult-dystopian novel written by Lois Lowry and was published on September 25, 2000. A companion book to "The Giver" (1993), it is set in the same future time period and universe, treats some of the same themes, and is followed by "Messenger" (2004) and "Son" (2012) in "The Giver Quartet".


title: Gathering Blue

text: The central character, Kira, who has a deformed leg, is orphaned and must learn to survive in a society that normally leaves the weak or disabled exposed to die in the fields. In the course of the book, she begins to learn the art of dyeing thread to different colors except for blue, which nobody in her community knows how to make. She also learns more about the truth of her village and the terrible secrets that they hold.


title: Gathering Blue

text: The main character, Kira, who has a deformed leg, is recently orphaned since her mother abruptly died from unknown sickness, and her father died years ago on a hunt with the Hunters by being killed by The Beasts. Kira must learn to survive in a society that normally leaves the weak or disabled exposed to die in the fields.


title: Gathering Blue

text: Kira needs a reason for the council to keep her in the village and not to take her to the Field, which is certain death at the hands of The Beasts. A member of the council, Jamison, defends Kira during the trial, much to Kira's surprise, and convinces the Council that Kira has a gift for embroidery. She is found worthy of life in society at the trial and is given the task of repairing the Singer's robe.


title: Gathering Blue

text: She is taught how to further solidify her talent from a much older woman, Annabella, who continues to teach Kira how to create dyes for different shades and hues for her thread work. To Kira's dismay, she learns that there is no ability to create the color blue for the threads that she will be using. Eventually, to Kira's surprise, Annabella tells her that with her own years and knowledge, she knows much of the society's history and even goes so far as to say that there really are no Beasts, contrary to the society's beliefs. Kira is unsure what to think of that revelation or what Annabella really means by it.


title: Gathering Blue

text: Along the way, she becomes closer friends with a younger boy, Matt, and makes a new friend in her neighborhood at her new home, Thomas, who is a boy around Kira's age. Thomas is also an orphan and has lived there since he was very young because of his abilities. Kira learns that he is the woodworker who maintains and improves the Singer's staff, which, in turn, helps the Singer remember the history of the society as he sings the lengthy song. Together, they help each other bring out the best in their talents to prepare for The Gathering. Jamison, the Guardian who fought for her life in the trial, becomes somewhat of a mentor in her new home. He is kind and instructive but also very stern.


title: Gathering Blue

text: Kira slowly learns that her life is less than idyllic. Thomas hears crying in her building, and they discover another orphan, a very young girl, Jo, whose ability to sing is magnificent. She is kept with the intent of eventually replacing the current Singer. Jo is scolded and punished if she does not sing. Kira secretly befriends her and sneaks into Jo's locked room at night to comfort her. Kira realizes that the three do not have as much freedom as they had previously thought. Annabella abruptly dies, and Matt tells Kira that the old dyer had died and been dragged to the Field by Jamison and his men. Kira is later told that Annabella had died of old age and died while asleep by Jamison. Kira is left to continue her work. That and the secluded life that a very young Jo must live help Kira decide to find out the truth about her society.


title: Gathering Blue

text: On the day that the Singer sings the Song at the Gathering, Matt is nowhere to be found. At the Ceremony of the Gathering, she notices that the current Singer both uses the staff that Thomas has worked so hard on and wears the robe that she repaired and enhanced. She realizes that his feet are chained, scarred, and bleeding. This implies that he is essentially a prisoner kept for the Ceremony because of his talent. This implies that Kira and the others with Gifts, which the council has saved for their jobs, are also prisoners. Their gifts are in control of the council by tenants who, without any creativity of their own, seek to control the three to provide a future that they envision.


title: Gathering Blue

text: After a long absence, Matt returns with a blind man from the distant Village of Healing. The man wears a blue shirt, which Kira's people are unable to make. The man is Kira's father, Christopher, who Kira long thought dead. Christopher reveals that he had been attacked years earlier by another hunter, who was jealous of his immediate potential of being a member on the Council of the Guardians. He was beaten and stabbed, blinding him. After being taken to the fields to die with the other rejected, injured, and dying citizens of their society, he was rescued by some people he could not see. They took him to the Village that he now lives in. This village is full of kind and helpful people, as opposed to the selfish residents of Kira's village. Matt excitedly explains that they know the way to make blue threads, and he brings plants that will allow Kira to do the same.


title: Gathering Blue

text: After a long heartfelt reunion with his daughter, Christopher reveals that he has enemies on the council. The one who maimed him years before was none other than Jamison. He tearfully apologizes for taking so long to return to get her. Because of his memory loss caused by the beating and his loss of sight, he had no way of finding her. Matt had gone looking for a way to make blue for Kira and stumbled upon Christopher's village, leading to this eventual reunion.


title: Gathering Blue

text: Kira begins to wonder if her mother's sudden death and the deaths of the two other orphans' parents were actually by the council's hand to acquire the young gifted children so that it could mould them into creating the future that it wants.


title: Gathering Blue

text: Christopher cannot stay and is forced to return to his village. Kira, however, decides to stay in her own community to continue to embroider the Singer's robe and help improve her society. Matt is designated as the "eyes" that will help Christopher find his way back. It is implied that Thomas, Kira, and Jo, who are the new holders of the Gifts, have the opportunity to change the cycle of their society and to improve the conditions in which they live by using their gifts to influence the actions of their people vastly.


title: Gathering Blue

text: At the end of the book, Matt tells Kira that in the Village, all are important and married, which she would have to do without in her society in which the injured and the impaired are seen as worthless wastes of space. He continues to tell her about a boy from the Village who has blue eyes, is around her age, and is not injured in any way (alluding to Jonas from "The Giver") in the hope that will entice her to come with them. Kira declines to go with them to the Village, but it is decided that she will follow once her work in her current task is eventually finished. In the meantime, Matt will travel back and forth between Kira and her father Christopher, being called their Messenger, relaying their messages.


title: Gathering Blue

text: The book appeared in the 9th spot on the Children's Books version of "The New York Times" Best seller list on October 8, 2000, and again on October 29, this time in the tenth spot. Gathering Blue also received the 2001 award for Selected Audiobooks for Young Adults.


title: Danny Kirwan

text: Daniel David Kirwan (13 May 1950 – 8 June 2018) was a British musician whose greatest success came with his role as guitarist, singer and songwriter with the blues rock band Fleetwood Mac between 1968 and 1972. He released three albums as a solo artist from 1975 to 1979, recorded albums with Otis Spann, Chris Youlden, and Tramp, and worked with his former Fleetwood Mac colleagues Jeremy Spencer and Christine McVie on some of their solo projects. As a member of Fleetwood Mac, he was inducted into the Rock and Roll Hall of Fame in 1998.


title: Danny Kirwan

text: Danny Kirwan was born Daniel David Langran on 13 May 1950 and grew up in Brixton, South London. His parents separated when he was young. His mother, Phyllis Rose Langran, married Aloysious J. Kirwan in 1958 when Danny was eight. Kirwan left school in 1967 with six O-levels and worked for a year as an insurance clerk in Fenchurch Street in the City of London.


title: Danny Kirwan

text: His mother was a singer and he grew up listening to the music of jazz musicians such as Eddie Lang, Joe Venuti, Belgian gypsy guitarist Django Reinhardt and 1930s–40s groups such as the Ink Spots. He began learning guitar at the age of 15 and became an accomplished self-taught guitarist and musician, influenced by, among others, Hank Marvin of the Shadows, Django Reinhardt, Jimi Hendrix, and particularly by Eric Clapton's playing in the Bluesbreakers. Kirwan was 17 when he came to the attention of established British blues band Fleetwood Mac in London while fronting his first band Boilerhouse, a blues three-piece with Trevor Stevens on bass guitar and Dave Terrey on drums. Boilerhouse played support slots for Fleetwood Mac at London venues such as the Nag's Head in Battersea and John Gee's Marquee Club in Wardour Street.


title: Danny Kirwan

text: Fleetwood Mac had been constituted as a quartet, but Green had been looking for another guitarist because slide guitarist Jeremy Spencer did not contribute to his songs. The band's drummer Mick Fleetwood, previously a member of John Mayall and the Bluesbreakers (as were Peter Green and bass player John McVie), was impressed by Kirwan's playing and suggested that he could join Fleetwood Mac. Although the rest of the band were not entirely convinced, Fleetwood invited Kirwan to join the band in August 1968. Kirwan's reaction was described as "astonishment and delight."


title: Danny Kirwan

text: Green had wanted to move Fleetwood Mac away from pure blues and needed a new musical collaborator and backing guitarist to work with. "Which is how Danny Kirwan came into our lives," Fleetwood recalled. "Danny was a huge fan of Peter's. He would see us every chance he got, usually watching in awe from the front row." Kirwan would often turn up at gigs during the afternoon, help to carry the gear in and jam with Green after the soundcheck.


title: Danny Kirwan

text: Fleetwood Mac's producer Mike Vernon was impressed by Kirwan's guitar playing and subtle vibrato and thought he sounded like blues player Lowell Fulson. Vernon said, "Danny was outstanding. He played with an almost scary intensity. He had a guitar style that wasn't like anyone else I'd heard in England."


title: Danny Kirwan

text: Fleetwood said, "Danny was an exceptional guitar player. It was clear that he needed to be with better players ... In the end, we just invited him to join us. It was one of those 'ah-ha' moments when you realise the answer is right there in front of you." Kirwan's arrival expanded Fleetwood Mac to a five-piece with three guitarists.


title: Danny Kirwan

text: Green described Kirwan as "a clever boy who got ideas for his guitar playing by listening to all that old-fashioned Roaring Twenties big-band stuff." Kirwan was known to be "emotionally fragile", and Green said that in the early days, Kirwan "was so into it that he cried as he played."


title: Danny Kirwan

text: Mick Fleetwood described the early Fleetwood Mac as it was when Kirwan joined the band. "We were a rude, wild, fun-loving bunch of people ... Fleetwood Mac never wanted to be pure blues like John Mayall, or rock like Hendrix or Cream. We were a funny, vulgar, drunken, vaudeville blues band at that time [1967–70], playing music as much to amuse ourselves as to please an audience."


title: Danny Kirwan

text: A year after forming Fleetwood Mac, Peter Green was looking for ways to extend the band and perhaps change its direction. He wanted to be open to other musical styles and bring in more original material. Kirwan was the ideal foil for Green's new approach; he played gentle, supportive rhythm guitar to Green and Spencer's fiery solo work and introduced vocal harmonies to some of the songs. Spencer said, "Peter and I had seen Danny play and thought he was very good. Peter and Danny worked well together."


title: Danny Kirwan

text: Fleetwood said, "Danny worked out great from the start. His playing was always very melodic and tuneful, with lots of bent notes and vibrato. Danny's style of playing complemented Peter's perfectly because he was already a disciple. His sense of melody on rhythm guitar really drew Peter out, allowing him to write songs in a different style. He was full of ideas that helped to move Fleetwood Mac out of the blues and into the rock mainstream ... Playing live, he was a madman." Fleetwood Mac biographer Leah Furman said Kirwan "provided a perfect sounding board for Peter's ideas, added stylistic texture, and moved Fleetwood Mac away from pure blues."


title: Danny Kirwan

text: Kirwan was interviewed by weekly music paper "Melody Maker" soon after joining Fleetwood Mac and gave the first indication of the breadth of his musical influences. He told "Melody Maker", "I'm not keen on blues purists who close their ears to all other forms of music. I like any good music, particularly the old big band-type things. Django Reinhardt is my favourite guitarist, but I like any music that is good, whether it is blues, popular or classical."


title: Danny Kirwan

text: The band's manager Clifford Davis, himself a musician, remembered Kirwan as "a very bright boy with very high musical standards. When we were on the road he was constantly saying 'Come on, Clifford, we must rehearse, we must rehearse, we've got to rehearse'." Davis said Kirwan "was the originator of all the ideas regarding harmonies and the lovely melodies that Fleetwood Mac would eventually encompass."


title: Danny Kirwan

text: Kirwan progressed from being an 18-year-old guitarist in a small pub band in south London to being a member of an internationally known touring band in one move. He played his first gig with Fleetwood Mac on 14 August 1968 at the Nag's Head Blue Horizon Club in Battersea, London. Ten days later he was on stage at the Hyde Park Free Concert in London, performing on the same bill as Family, Ten Years After and Fairport Convention. Two days later he was in the BBC radio studios in London with the band, recording a session of twelve songs for broadcast on John Peel's 'Top Gear'. Three days after that Fleetwood Mac began a 50-date tour of the UK and Scandinavia, and at the end of November they were in Paris, performing in a New Year's Eve show for French television "[ORTF 'Surprise Partie']" with The Who, Small Faces, Pink Floyd and The Troggs. Two days later, on 1 December 1968, Kirwan was in New York City at the start of an almost sold-out, 30-date Fleetwood Mac US tour which would include performances at major venues such as the Fillmore East in Manhattan, the Fillmore West in San Francisco, the Boston Tea Party, and an appearance before 100,000 fans at the three-day Miami Pop Festival in Florida alongside, among others, Chuck Berry, Muddy Waters, BB King, and The Grateful Dead. In April 1969, Kirwan played at the Royal Albert Hall in London when Fleetwood Mac supported BB King on the opening date of his first UK tour. The band had opened a show for BB King in Chicago in January, and played support on the eight-date UK tour.


title: Danny Kirwan

text: Kirwan toured several times with Fleetwood Mac in Europe. Fleetwood said in his autobiography, "We were "huge" in Europe. Even a simple blues track like "Shake Your Moneymaker" went to the top of the charts in Scandinavia. Every place we played was sold out and raving."


title: Danny Kirwan

text: Kirwan's first recorded work with Fleetwood Mac, in October 1968, was his contribution of the second guitar part to Green's instrumental hit single "Albatross". Green had been working on the piece for some time, and Kirwan completed it by adding the counterpoint harmony in the middle section. Green said, "Once we got Danny in, it was plain sailing... I would never have done 'Albatross' if it wasn't for Danny. I would never have had a number one hit record." Kirwan said Green had told him what to do and all the bits he had to play.


title: Danny Kirwan

text: The band spent two days recording and mixing the track at CBS studios in New Bond Street, London, and when they listened to the final mix, everyone agreed it was "a beautiful record". "Albatross" was released in November 1968 on Mike Vernon's Blue Horizon label. It reached number one in the UK singles charts in December 1968 and sold nearly a million copies.


title: Danny Kirwan

text: The B-side of "Albatross" was Kirwan's first published tune, the instrumental "Jigsaw Puzzle Blues". This was an old clarinet piece, written by Joe Venuti and Adrian Rollini and recorded by the Joe Venuti / Eddie Lang Blue Five in 1933. Kirwan worked out the piece from the record and adapted it for Green and himself to play on guitar, but Green remembered, "I couldn't do it properly. I can't play that sort of big-band type thing. My style wasn't all that satisfactory to Danny, but his style wasn't all that satisfactory to me." So Kirwan played all the guitar parts himself.


title: Danny Kirwan

text: The Beatles admired "Albatross" and were inspired by it to create the slow, melodic, harmonised track "Sun King" on their 1969 album "Abbey Road". In the spring of 1969, after Fleetwood Mac's manager had removed the band from the Blue Horizon label, John Lennon was reported to be interested in signing Fleetwood Mac to the Beatles' new Apple Records label. The band eventually signed to Warner Bros. Records.


title: Danny Kirwan

text: In early January 1969 Kirwan was on his first tour of the United States with Fleetwood Mac, and they opened for Muddy Waters at the Regal Theater in Chicago. While they were there, producer Mike Vernon heard that Chess Records was about to close its famous Chicago studio and suggested recording a Fleetwood Mac blues album in the home of Chicago blues before it disappeared. He and Marshall Chess arranged a two-day recording session in which Kirwan, along with Green, Spencer, McVie and Fleetwood, played with legendary blues musicians David 'Honeyboy' Edwards, Walter 'Shakey' Horton, J.T. Brown, Willie Dixon, Otis Spann, Buddy Guy, and S.P. Leary. Willie Dixon organised the sessions.


title: Danny Kirwan

text: The recordings made at Chess Studios were judged a great success and were released by Vernon in December 1969 as a double album on the Blue Horizon label, originally entitled "Blues Jam at Chess" and later reissued as "Fleetwood Mac in Chicago". Fleetwood said later that the sessions had produced some of the best blues the band had ever played, and ironically, the last blues that Fleetwood Mac would ever record. Two of Kirwan's songs, "Talk With You" and "Like It This Way", were included on the album.


title: Danny Kirwan

text: Kirwan's skills came further to the forefront on the mid-1969 album "Then Play On", recorded at Kingsway Studios in Holborn, London. Green had told Kirwan when he joined the band that he would be responsible for half of the next album, and the songwriting and lead vocals on "Then Play On" were split almost equally between the two guitarists, with many of the performances featuring their dual lead Gibson Les Paul guitars. Fleetwood said that Kirwan, asked to write his first songs for the band, "approached his assignment very cerebrally, much as Lindsey Buckingham would do later, and came up with some very good music." [Fleetwood said many years later in an interview that Buckingham had "a huge regard for Danny".] Kirwan's input drew on material he had written in his first band.


title: Danny Kirwan

text: Green took a back seat during the recording sessions and left most of the guitar work to Kirwan. Spencer did not play guitar or sing on the album and Kirwan had a significant role in the recording. He composed seven of the 14 tracks and his "Coming Your Way" opened side one of the album. His varied musical influences were evident throughout, from the flowing instrumental "My Dream" to the 1930s-style "When You Say", which Green had earmarked to be a single until his own composition "Oh Well" took shape and was chosen instead. "Coming Your Way" was a full band performance and "Like Crying" was a Kirwan duet with Green. Kirwan played all the guitar parts on "Although the Sun is Shining". Mike Vernon noted that Kirwan's presence and his eclectic musical influences "were already beginning to take the band out of mainstream 12-bar blues and into blues-rock and rock ballads."


title: Danny Kirwan

text: The UK release of "Then Play On" featured two extra earlier Kirwan recordings, the sad blues "Without You" and the heavy "One Sunny Day", which was later covered by American blues musician Tinsley Ellis on his 1997 album "Fire It Up". "Then Play On" was released in September 1969 and reached number five in the UK album charts. It was the band's first album to sell more than 100,000 in America.


title: Danny Kirwan

text: In December 1969, 16 months after Kirwan joined the band, Fleetwood Mac were voted the UK's number-one progressive group in "Melody Maker's" end-of-year polls. The band had also outsold the Beatles and the Rolling Stones in Europe in record sales and concert tickets.


title: Danny Kirwan

text: The US-only release "English Rose" from the same era included Kirwan's "Without You" and "One Sunny Day", plus his tense blues "Something Inside of Me" and "Jigsaw Puzzle Blues", both also dating from earlier sessions. Fleetwood described the album as "a sort of pastiche" consisting of the best cuts from their second studio album, "Mr Wonderful", plus "Black Magic Woman", "Albatross", and the four new tracks from Kirwan. "English Rose" was Fleetwood Mac's second album release in the US. Kirwan began a two-month tour with the band to promote "English Rose" at the Fillmore East in New York on 1 February 1969.


title: Danny Kirwan

text: The US track-listing of "Then Play On" was reordered to allow the inclusion of the full nine-minute version of Green's hit single "Oh Well", and two of Kirwan's songs, "My Dream" and "When You Say", were dropped. Only "Coming Your Way", the wistful "Although the Sun Is Shining" and his duet with Green, "Like Crying", appeared on all the later non-UK vinyl releases.


title: Danny Kirwan

text: On the 1990 CD release, Kirwan's two dropped songs were reinstated, although "One Sunny Day" and "Without You" were now absent from releases in all territories, including the UK. The 2013 CD release restored the original UK track order, with "Without You" and "One Sunny Day" included.


title: Danny Kirwan

text: Archival packages from this era such as "The Vaudeville Years" and "Show-Biz Blues" double sets include several Kirwan songs and show his blues influences, as well as the more arcane tastes that led to songs such as "Tell Me from the Start", which could have been mistaken for a song by the 1920s-style group The Temperance Seven. Kirwan's unusual musical interests are said to have prompted band leader Green to dub him "Ragtime Cowboy Joe".


title: Danny Kirwan

text: The track listing on "The Vaudeville Years" contained five of Kirwan's songs: "Like It This Way", "Although the Sun Is Shining", "Love It Seems", "Tell Me from the Start", and "Farewell", plus his joint composition with Green, "World in Harmony". His songs on "Show-Biz Blues" were "Mind of My Own" and a live version of "Coming Your Way". Kirwan's up-tempo blues "Like It This Way" was recorded during the "Man of the World" sessions early in 1969. It was the first Fleetwood Mac recording to feature Kirwan and Green's duelling twin-lead guitars, which later became part of the band's live performances.


title: Danny Kirwan

text: Fleetwood Mac's hit singles from 1968 to 1970 were all written by Green but Kirwan's style shone through, thanks to Green's desire not to act as the band's main focus. Kirwan joined Green in the dual guitar harmonies on "Albatross", contributed to "Man of the World" and took the solo on "Oh Well Pt. 1". Mike Vernon recalled "considerable input" from Kirwan in the making of "Man of the World", which was released in April 1969 and reached number two in the UK charts.


title: Danny Kirwan

text: The final hit single from this line-up, "The Green Manalishi", was recorded in April 1970 in a difficult night-time session after Green had announced that he was leaving the band. Producer Martin Birch recalled Green growing increasingly frustrated at the results of the session because he could not get the sound he wanted, and Kirwan reassuring him that they would stay there all night until they got it right. Green said later that although it had left him exhausted, making "Green Manalishi" was one of his best musical memories. "Lots of drums, bass guitars ... Danny Kirwan and me playing those shrieking guitars together ... I thought it would make number one."


title: Danny Kirwan

text: The track was recorded at Warner-Reprise's studios in Hollywood on the band's third US tour. "The Green Manalishi" was released in May 1970 and reached number 10 in the UK charts. It was the band's fourth consecutive hit single, and Fleetwood Mac's last in the UK for six years.


title: Danny Kirwan

text: The B-side of "The Green Manalishi" was the instrumental "World in Harmony", the only track ever given a "Kirwan/Green" joint songwriting credit. In March 1970, Green said that he and Kirwan were planning an album based around their two guitars, and Spencer recalled later that Kirwan and Green had begun to piece their guitar parts together "almost like orchestrally layered guitar work."


title: Danny Kirwan

text: Kirwan and Green had already worked on melodic twin guitar demos that had sparked rumours in the music press in late 1969 of a duelling guitars project, but ultimately nothing came of it.


title: Danny Kirwan

text: Despite the closeness of their musical partnership, Kirwan and Green did not always get on well personally, which was at least partly due to Kirwan's short temper. Kirwan had high musical standards and concentrated more on rehearsing than the other members of the band, with Green recalling that Kirwan always had to arrive anywhere an hour early, but Green was more talented when it came to improvisational skills.


title: Danny Kirwan

text: One of the band's roadies, Dennis Keane, recalled that Kirwan had begun to clash with Green. He suggested that perhaps the success of "Albatross" and the follow-up single "Man of the World" had gone to his head and he had become more confident, to the point of trying to pressure Green and compete with him. Producer Martin Birch, however, remembered Kirwan often seeking reassurance from Green and said he was always in awe of him. "I often got the impression that Danny was looking for Peter's approval, whereas Peter wanted Danny to develop by himself."


title: Danny Kirwan

text: After rumours in the music press in early 1970 that Kirwan would leave Fleetwood Mac, it was Green who departed, in May of that year. Kirwan later said that he was not surprised. "We just didn't get on too well basically ... We played some good stuff together, we played well together, but we didn't get on." Brunning said in his 1998 history of the band that Green left because of personality clashes with Kirwan and musical and personal differences with the other band members. He said Green wanted to be free to play with other musicians and not be tied down to a particular musical format.


title: Danny Kirwan

text: In January 1969, Kirwan made his first musical appearance outside Fleetwood Mac when he contributed to Otis Spann's blues album "The Biggest Thing Since Colossus" with Green and John McVie. After "Then Play On" had been completed, Kirwan worked on Christine McVie's first solo album, titled "Christine Perfect" (McVie was then still using her maiden name). She included a version of Kirwan's "When You Say" on the album, which was chosen as a single. Kirwan arranged the string section and acted as producer.


title: Danny Kirwan

text: Kirwan worked with Fleetwood and John McVie on the first solo album from a then-current member of Fleetwood Mac when Spencer recorded his album "Jeremy Spencer", released in January 1970. Kirwan played rhythm guitar in various styles and sang backing vocals throughout. The album was not commercially successful, but Spencer discovered that he and Kirwan worked well together without Green. He said later, "In retrospect, one of the most enjoyable things was working with Danny on it, as it brought out a side of him I hadn't seen."


title: Danny Kirwan

text: In 1969, Kirwan contributed as a session guitarist to the first album by London-based blues band Tramp, titled "Tramp", which was recorded at DeLane Lea Studios in Soho. The album featured an uptempo guitar instrumental, "Hard Work", from Kirwan. Mick Fleetwood played drums on the recording.


title: Danny Kirwan

text: Tramp's bass player Bob Brunning, Fleetwood Mac's first bassist, said he had enjoyed working with Kirwan during the Tramp sessions and remembered him being friendly and cooperative. In his 1998 history of the band, Brunning described Kirwan as a talented and soulful musician who had contributed much fine work to Fleetwood Mac's repertoire. He recalled that when his bass amplifier was stolen in 1969, Kirwan had given him a vintage Marshall amp as a replacement.


title: Danny Kirwan

text: After Green left in May 1970 the band considered splitting up. Kirwan and Spencer were now having to front the band and their morale was low. Fleetwood said Spencer was terrified of being a front man on his own, "and the pressure on Danny's sensitive temperament was tremendous." He recalled, "There was one terrible night when everybody decided they wanted to leave ... but one by one, I talked them all back in." They continued briefly as a four-piece and were rescued after the recording of "Kiln House" by the arrival of keyboard player Christine McVie, described by Fleetwood as "the best blueswoman in England", as a fifth band member. Fleetwood said, "Christine became the glue ... she filled out our sound beautifully."


title: Danny Kirwan

text: The new line-up included some of McVie's songs, introduced vocal harmonies, continued to showcase Spencer's talents and allowed Kirwan to develop more melodic rock. McVie played her first official gig with Fleetwood Mac on 1 August 1970 at The Warehouse in New Orleans, Louisiana, at the start of a three-month US tour.


title: Danny Kirwan

text: Kirwan and Spencer handled the guitars and vocals together on the "Kiln House" album, released in September 1970, and continued the working relationship they had developed during the recording of Spencer's solo album the previous year. Kirwan's songs on "Kiln House" included "Station Man", co-written with Spencer and John McVie, which became a live staple into the post-1974 Buckingham-Nicks era.


title: Danny Kirwan

text: His other songs on the album were "Jewel-Eyed Judy", dedicated to Judy Wong, a friend of the band from San Francisco; the energetic "Tell Me All the Things You Do"; and "Earl Gray", an atmospheric instrumental that Kirwan had largely composed while Peter Green was still in the band. Kirwan also sang distinctive backing vocals on some of Spencer's numbers, such as the 1950s-flavoured opening track "This Is the Rock". Christine McVie played keyboards and sang backing vocals, uncredited, on the album.


title: Danny Kirwan

text: Other Kirwan compositions from the second half of 1970, such as those which eventually surfaced in the 2003 "Madison Blues" CD box set, included "Down at the Crown". The lyrics referred to a pub near the band's communal house, 'Benifold', in Headley, Hampshire. The unsuccessful single "Dragonfly", recorded late in the year, was written by Kirwan and included lyrics adapted from a poem by W. H. Davies. This was not the last time Kirwan used a poem as lyrics for a song, and may have been a solution to occasional lack of inspiration. The B-side of the single, "The Purple Dancer", written by Kirwan, Fleetwood, and John McVie, featured Kirwan and Spencer duetting on lead vocals.


title: Danny Kirwan

text: Two tours of the US followed in support of "Kiln House", but the second, in February 1971, was blighted by Jeremy Spencer's bizarre departure from the group. He disappeared from the band's hotel in Los Angeles on the afternoon of a sold-out gig at the prestigious Whisky a Go Go, which had to be cancelled, and after several days of frantic searching was discovered to have joined the California-based religious cult the Children of God.