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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