A note on $ p $-supersolubility of finite groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866915018519347200 |
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| author | Qiu, Zhengtian Chen, Guiyun Liu, Jianjun |
| author_facet | Qiu, Zhengtian Chen, Guiyun Liu, Jianjun |
| contents | Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies $ \mathscr L $-$ Π$-property in $ G $ if $ | G / K : N _{G / K} (HK/K)| $ is a $ π(HK/K) $-number for all maximal $ G $-invariant subgroup $ K $ of $ H^{G} $. In this paper, we give a characterization of finite $p$-supersoluble groups under assumption that some subgroups of prime power order satisfy $ \mathscr L $-$ Π$-property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09814 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on $ p $-supersolubility of finite groups Qiu, Zhengtian Chen, Guiyun Liu, Jianjun Group Theory Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies $ \mathscr L $-$ Π$-property in $ G $ if $ | G / K : N _{G / K} (HK/K)| $ is a $ π(HK/K) $-number for all maximal $ G $-invariant subgroup $ K $ of $ H^{G} $. In this paper, we give a characterization of finite $p$-supersoluble groups under assumption that some subgroups of prime power order satisfy $ \mathscr L $-$ Π$-property. |
| title | A note on $ p $-supersolubility of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2310.09814 |