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 ${\gamma }_k$-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.

7 pages

References in corpus (1)

• Outer commutator words are uniformly concise

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