Indices of non-supersolvable maximal subgroups in finite groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910913813020672 |
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| author | Beltrán, Antonio Shao, Changguo |
| author_facet | Beltrán, Antonio Shao, Changguo |
| contents | Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared prime index. In this note we describe the structure of the non-solvable finite groups whose maximal subgroups are either supersolvable or have prime or squared prime index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indices of non-supersolvable maximal subgroups in finite groups Beltrán, Antonio Shao, Changguo Group Theory 20E28 20D15 20D06 Two classic results, due to K. Doerk and P. Hall respectively, establish the solvability of those finite groups all of whose maximal subgroups are supersolvable, and the solvability of finite groups in which all maximal subgroups have prime or squared prime index. In this note we describe the structure of the non-solvable finite groups whose maximal subgroups are either supersolvable or have prime or squared prime index. |
| title | Indices of non-supersolvable maximal subgroups in finite groups |
| topic | Group Theory 20E28 20D15 20D06 |
| url | https://arxiv.org/abs/2501.04537 |