CONCISENESS OF COPRIME COMMUTATORS IN FINITE GROUPS

Abstract

AbstractLet$G$be a finite group. We show that the order of the subgroup generated by coprime${\gamma }_{k} $-commutators (respectively,${\delta }_{k} $-commutators) is bounded in terms of the size of the set of coprime${\gamma }_{k} $-commutators (respectively,${\delta }_{k} $-commutators). This is in parallel with the classical theorem due to Turner-Smith that the words${\gamma }_{k} $and${\delta }_{k} $are concise.