Commutators of elements of coprime orders in finite groups

2012/08/15 by Shumyatsky, Pavel · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1208.3177

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.

Cited by

• Coprime commutators in profinite groups

Related

• Commutators between coprime order elements in non-abelian simple groups
• Strong conciseness of coprime and anti-coprime commutators
• Coprime commutators in finite groups
• Criteria for solubility and nilpotency of finite groups with automorphisms
• Coprime automorphisms of finite groups