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arXiv · 2608.01754

The problem of recognition of finite simple groups by element orders is solved

Maria A. Grechkoseeva·Alexey M. Staroletov·Andrey V. Vasil'ev
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Abstract

For a finite group $G$, let $ω(G)$ be the set of element orders of $G$ and let $h(G)$ be the number of pairwise nonisomorphic finite groups $H$ with $ω(H)=ω(G)$. We say that the recognition problem is solved for $G$ if the number $h(G)$ is known, and if it is finite, then all finite groups $H$ with $ω(H)=ω(G)$ are listed. We complete the solution of the recognition problem for all finite simple groups.

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Maria A. Grechkoseeva, Alexey M. Staroletov, Andrey V. Vasil'ev. 2026-08-03. The problem of recognition of finite simple groups by element orders is solved. https://arxiv.org/abs/2608.01754

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