A note on the $ Π$-property of some subgroups of finite groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914868769062912 |
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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 $ Π$-property in $ G $ if for any chief factor $ L / K $ of $ G $, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $ π(HK/K\cap L/K) $-number. In this paper, we obtain some criteria for the $ p $-supersolubility or $ p $-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $ Π$-property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the $ Π$-property of some 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 $ Π$-property in $ G $ if for any chief factor $ L / K $ of $ G $, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $ π(HK/K\cap L/K) $-number. In this paper, we obtain some criteria for the $ p $-supersolubility or $ p $-nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the $ Π$-property. |
| title | A note on the $ Π$-property of some subgroups of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2405.05106 |