On the partial $Π$-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909138671370240 |
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| author | Qiu, Zhengtian Liu, Jianjun Chen, Guiyun |
| author_facet | Qiu, Zhengtian Liu, Jianjun Chen, Guiyun |
| contents | Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ Π$-property in $ G $ if if there exists a chief series $ \varGamma_{G}: 1 =G_{0} < G_{1} < \cdot\cdot\cdot < G_{n}= G $ of $ G $ such that for every $ G $-chief factor $ G_{i}/G_{i-1} $ $ (1\leq i\leq n) $ of $ \varGamma_{G} $, $ | G / G_{i-1} : N_{G/G_{i-1}} (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1})| $ is a $ π(HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1}) $-number. In this paper, we study the influence of some second minimal or second maximal subgroups of a Sylow subgroup satisfying the partial $ Π$-property on the structure of a finite group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the partial $Π$-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups Qiu, Zhengtian Liu, Jianjun Chen, Guiyun Group Theory Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the partial $ Π$-property in $ G $ if if there exists a chief series $ \varGamma_{G}: 1 =G_{0} < G_{1} < \cdot\cdot\cdot < G_{n}= G $ of $ G $ such that for every $ G $-chief factor $ G_{i}/G_{i-1} $ $ (1\leq i\leq n) $ of $ \varGamma_{G} $, $ | G / G_{i-1} : N_{G/G_{i-1}} (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1})| $ is a $ π(HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1}) $-number. In this paper, we study the influence of some second minimal or second maximal subgroups of a Sylow subgroup satisfying the partial $ Π$-property on the structure of a finite group. |
| title | On the partial $Π$-property of second minimal or second maximal subgroups of Sylow subgroups of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2304.11451 |