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arXiv · 1208.3177

Commutators of elements of coprime orders in finite groups

Pavel Shumyatsky
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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.

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Pavel Shumyatsky. 2012-08-15. Commutators of elements of coprime orders in finite groups. https://arxiv.org/abs/1208.3177

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