Commutators between coprime order elements in non-abelian simple groups

Fuente: arXiv
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Main Authors: Lucchini, Andrea, Spiga, Pablo
Format: Preprint
Published: 2025
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author Lucchini, Andrea
Spiga, Pablo
author_facet Lucchini, Andrea
Spiga, Pablo
contents 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 $g\in G$, there exist $x,y\in G$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_02330
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Commutators between coprime order elements in non-abelian simple groups
Lucchini, Andrea
Spiga, Pablo
Group Theory
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 $g\in G$, there exist $x,y\in G$ 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.
title Commutators between coprime order elements in non-abelian simple groups
topic Group Theory
url https://arxiv.org/abs/2504.02330