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.
Conciseness of coprime commutators in finite groups / Acciarri, C; Shumyatsky, P; Thillaisundaram, A. - In: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 0004-9727. - 89:2(2014), pp. 252-258. [10.1017/S0004972713000361]
Conciseness of coprime commutators in finite groups
Acciarri C;
2014
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.
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