Conciseness of coprime commutators in finite groups

Abstract

Let G be a finite group. We show that the order of the subgroup generated by coprime γk-commutators (respectively,δk- commutators) is bounded in terms of the size of the set of coprime γk-commutators (respectively, δk-commutators). This is in parallel with the classical theorem due to Turner-Smith that the words γk and δk are concise. ©2013 Australian Mathematical Publishing Association Inc.