Recognition by element orders for simple linear and unitary groups
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915917796999168 |
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| author | Grechkoseeva, Maria A. Staroletov, Alexey M. Vasil'ev, Andrey V. |
| author_facet | Grechkoseeva, Maria A. Staroletov, Alexey M. Vasil'ev, Andrey V. |
| contents | 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 $h(G)$ is finite, then all finite groups $H$ with $ω(H)=ω(G)$ are described. We complete the solution of the recognition problem for the finite simple linear and unitary groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_04587 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Recognition by element orders for simple linear and unitary groups Grechkoseeva, Maria A. Staroletov, Alexey M. Vasil'ev, Andrey V. Group Theory 20D06, 20D60 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 $h(G)$ is finite, then all finite groups $H$ with $ω(H)=ω(G)$ are described. We complete the solution of the recognition problem for the finite simple linear and unitary groups. |
| title | Recognition by element orders for simple linear and unitary groups |
| topic | Group Theory 20D06, 20D60 |
| url | https://arxiv.org/abs/2604.04587 |