On the maximal overgroups of Sylow subgroups of finite groups
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913263748382720 |
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| author | Baumeister, Barbara Burness, Timothy C. Guralnick, Robert M. Tong-Viet, Hung P. |
| author_facet | Baumeister, Barbara Burness, Timothy C. Guralnick, Robert M. Tong-Viet, Hung P. |
| contents | In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special case $r=2$. Several applications are presented. This includes some new results on weakly subnormal subgroups of finite groups, which can be used to study variations of the Baer-Suzuki theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13976 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the maximal overgroups of Sylow subgroups of finite groups Baumeister, Barbara Burness, Timothy C. Guralnick, Robert M. Tong-Viet, Hung P. Group Theory In this paper, we determine the finite groups with a Sylow $r$-subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special case $r=2$. Several applications are presented. This includes some new results on weakly subnormal subgroups of finite groups, which can be used to study variations of the Baer-Suzuki theorem. |
| title | On the maximal overgroups of Sylow subgroups of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2307.13976 |