For 10 points, name this group comprising all the permutations of a set of elements under composition.
Jucys-Murphy elements are used to study this group's representations, which include Specht modules. Jordan's Theorem states that if a primitive subgroup of this group has a cycle of prime length, it is either this group or a specific subgroup of it. The Robinson-Schensted correspondence bijects the elements of this group with Young tableaux, which George Frobenius applied to the study of this group. Any group G is isomorphic to a subgroup of this group acting on G according to Cayley's Theorem. A subgroup of this group comprising only the even elements is called the alternating group, and when this group acts on a set of n elements, it has cardinality n factorial. For 10 points, name this group comprising all the permutations of a set of elements under composition.
Jucys-Murphy elements are used to study this group's representations, which include Specht modules.
symmetric group [or S sub-n]