Commutators between coprime order elements in non-abelian simple groups

2025/04/03 by Lucchini, Andrea, Spiga, Pablo
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2504.02330

Abstract

Recent investigations on the set of commutators between the elements of a finite group having relatively prime orders have prompt us to propose a variant of the Ore conjecture: For every finite non-abelian simple group and for every g∈ G, there exist x,y∈ G with g=[y,x] and with the order of x relatively prime to the order of y. In this note we present some evidence towards the veracity of this conjecture by proving it for alternating groups and some sporadic simple groups.

Related

• Commutators of elements of coprime orders in finite groups
• On some conjectures related to finite nonabelian simple groups
• A counterexample for the conjecture of finite simple groups
• Finite simple groups have many classes of prime order elements
• Strong conciseness of coprime and anti-coprime commutators