Conciseness of coprime commutators in finite groups

C. Acciarri; P. Shumyatsky; A. Thillaisundaram

Conciseness of coprime commutators in finite groups

Authors

C. Acciarri University of Brasilia
P. Shumyatsky University of Brasilia
A. Thillaisundaram Otto-von-Guericke-Universitat Magdeburg

Keywords:

commutators, concise words

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. 10.1017/S0004972713000361

Author Biographies

C. Acciarri, University of Brasilia

Department of Mathematics

P. Shumyatsky, University of Brasilia

Department of Mathematics

A. Thillaisundaram, Otto-von-Guericke-Universitat Magdeburg

Faculty of Mathematics

Published

2014-01-27

Issue

Vol. 89 No. 2 (2014)

Section

Articles

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