On finite groups isospectral to groups with abelian Sylow $2$-subgroups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910098301911040 |
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| author | Grechkoseeva, M. A. Vasil'ev, A. V. |
| author_facet | Grechkoseeva, M. A. Vasil'ev, A. V. |
| contents | The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer $k$, we find $k$ nonabelian simple groups with abelian Sylow 2-subgroups such that their direct product is uniquely determined by its spectrum in the class of all finite groups. On the other hand, we prove that there are infinitely many finite groups having the same spectrum as the direct cube of the small Ree group $^2G_2(q)$, $q>3$, or the direct fourth power of the sporadic group $J_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finite groups isospectral to groups with abelian Sylow $2$-subgroups Grechkoseeva, M. A. Vasil'ev, A. V. Group Theory 20D60, 20D06, 20D08 The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer $k$, we find $k$ nonabelian simple groups with abelian Sylow 2-subgroups such that their direct product is uniquely determined by its spectrum in the class of all finite groups. On the other hand, we prove that there are infinitely many finite groups having the same spectrum as the direct cube of the small Ree group $^2G_2(q)$, $q>3$, or the direct fourth power of the sporadic group $J_1$. |
| title | On finite groups isospectral to groups with abelian Sylow $2$-subgroups |
| topic | Group Theory 20D60, 20D06, 20D08 |
| url | https://arxiv.org/abs/2409.15873 |