Year: 2025
Type: preprint
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 $g\in G$, 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.
Source: arXiv (Cornell University)
Authors: Lucchini, Andrea, Spiga, Pablo
Institutions: University of Padua, University of Milano-Bicocca
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: European Commission, NextGenerationEU
OpenAlex ID: W4415975198
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