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Commutators of elements of coprime orders in finite groups

  • Pavel Shumyatsky EMAIL logo
Published/Copyright: February 20, 2013

Abstract

This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in terms of such commutators is obtained. We also conjecture that every element of a nonabelian simple group is a commutator of elements of coprime orders and we confirm this conjecture for the alternating groups.

Received: 2012-8-24
Revised: 2012-10-27
Published Online: 2013-2-20
Published in Print: 2015-1-1

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