Commutators of elements of coprime orders in finite groups
Group Theory
2012-08-17 v2
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.
Keywords
Cite
@article{arxiv.1208.3177,
title = {Commutators of elements of coprime orders in finite groups},
author = {Pavel Shumyatsky},
journal= {arXiv preprint arXiv:1208.3177},
year = {2012}
}