Pavel Shumyatsky
Published 2012-08-15, updated 2012-08-16Version 2
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.
On the number of $p$-elements in a finite group
The Chebotarev invariant of a finite group: a conjecture of Kowalski and Zywina
A conjecture on B-groups
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