Determining hypercentral Hall subgroups in finite groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911974314475520 |
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| author | Sotomayor, Víctor |
| author_facet | Sotomayor, Víctor |
| contents | Let $G$ be a finite group, and let $π$ be a set of primes. The aim of this paper is to obtain some results concerning how much information about the $π$-structure of $G$ can be gathered from the knowledge of the lengths of conjugacy classes of its $π$-elements and of their multiplicities. Among other results, we prove that this multiset of class lengths determine whether $G$ has a hypercentral Hall $π$-subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Determining hypercentral Hall subgroups in finite groups Sotomayor, Víctor Group Theory 20D15, 20D20, 20E45 Let $G$ be a finite group, and let $π$ be a set of primes. The aim of this paper is to obtain some results concerning how much information about the $π$-structure of $G$ can be gathered from the knowledge of the lengths of conjugacy classes of its $π$-elements and of their multiplicities. Among other results, we prove that this multiset of class lengths determine whether $G$ has a hypercentral Hall $π$-subgroup. |
| title | Determining hypercentral Hall subgroups in finite groups |
| topic | Group Theory 20D15, 20D20, 20E45 |
| url | https://arxiv.org/abs/2403.00583 |