 In formula_59 there are the subgroupsformula_60Notice formula_61, hence the Borel group has the formformula_62

In the product group formula_63 the Borel subgroup can be represented by matrices of the formformula_64where formula_65 is an formula_66 upper triangular matrix and formula_67 is a formula_68 upper triangular matrix.Any finite group whose "p"-Sylow subgroups are cyclic is a semidirect product of two cyclic groups, in particular solvable.Such groups are called Z-groups.