On the partial $ \mathscr L $-$ Π$-property of subgroups of finite groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909285986861056 |
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| author | Qiu, Zhengtian Ballester-Bolinches, Adolfo |
| author_facet | Qiu, Zhengtian Ballester-Bolinches, Adolfo |
| contents | Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ \mathscr L $-$ Π$-property in $ G $ if $ H\unlhd G $, or if $ | G / K : \mathrm{N} _{G / K} (HK/K)| $ is a $ π(HK/K) $-number for any $ G $-chief factor of type $ H^{G}/K $ with $ H_{G}\leq K $. In this paper, we investigate the structure of finite groups under the assumption that some subgroups of prime power order satisfy the partial $ \mathscr L $-$ Π$-property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the partial $ \mathscr L $-$ Π$-property of subgroups of finite groups Qiu, Zhengtian Ballester-Bolinches, Adolfo Group Theory Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ \mathscr L $-$ Π$-property in $ G $ if $ H\unlhd G $, or if $ | G / K : \mathrm{N} _{G / K} (HK/K)| $ is a $ π(HK/K) $-number for any $ G $-chief factor of type $ H^{G}/K $ with $ H_{G}\leq K $. In this paper, we investigate the structure of finite groups under the assumption that some subgroups of prime power order satisfy the partial $ \mathscr L $-$ Π$-property. |
| title | On the partial $ \mathscr L $-$ Π$-property of subgroups of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2408.06348 |