A Characterization of the Commutator Subgroup of a Group
G. Thierrin · Canadian Mathematical Bulletin · 1976
Abstract An element a of a semigroup S is n-potent if there exist a1, a2,..., ak∈S such that a = a1a2...ak and If S is a group, the set of n-potent elements is a normal subgroup of S and the set of 1-potent elements is the commutator subgroup of S.