Weakly subnormal subgroups and variations of the Baer-Suzuki theorem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914663547011072 |
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| author | Guralnick, Robert M. Tong-Viet, Hung P. Tracey, Gareth |
| author_facet | Guralnick, Robert M. Tong-Viet, Hung P. Tracey, Gareth |
| contents | A subgroup $R$ of a finite group $G$ is weakly subnormal in $G$ if $R$ is not subnormal in $G$ but it is subnormal in every proper overgroup of $R$ in $G$. In this paper, we first classify all finite groups $G$ which contains a weakly subnormal $p$-subgroup for some prime $p$. We then determine all finite groups containing a cyclic weakly subnormal $p$-subgroup. As applications, we prove a number of variations of the Baer-Suzuki theorem using the orders of certain group elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly subnormal subgroups and variations of the Baer-Suzuki theorem Guralnick, Robert M. Tong-Viet, Hung P. Tracey, Gareth Group Theory A subgroup $R$ of a finite group $G$ is weakly subnormal in $G$ if $R$ is not subnormal in $G$ but it is subnormal in every proper overgroup of $R$ in $G$. In this paper, we first classify all finite groups $G$ which contains a weakly subnormal $p$-subgroup for some prime $p$. We then determine all finite groups containing a cyclic weakly subnormal $p$-subgroup. As applications, we prove a number of variations of the Baer-Suzuki theorem using the orders of certain group elements. |
| title | Weakly subnormal subgroups and variations of the Baer-Suzuki theorem |
| topic | Group Theory |
| url | https://arxiv.org/abs/2402.00804 |