On the $IC$-$Π$-property of subgroups of finite groups
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908585208840192 |
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| author | Qiu, Zhengtian Qiao, Shouhong |
| author_facet | Qiu, Zhengtian Qiao, Shouhong |
| contents | Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the $ Π$-property in $ G $ if $ | G/K : N_{G/K}((H \cap L)K/K)| $ is a $ π(( H \cap L)K/K ) $-number for any chief factor $ L/K $ of $ G $; and we call that $ H $ satisfies the $ IC $-$ Π$-property in $ G $ if $ H\cap [H, G] $ satisfies the $ Π$-property in $ G $. In this paper, we obtain a criterion of a normal subgroup being contained in the $ p\mathfrak{U} $-hypercenter of a finite group by the $IC$-$ Π$-property of some $ p $-subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $IC$-$Π$-property of subgroups of finite groups Qiu, Zhengtian Qiao, Shouhong Group Theory Let $ H $ be a subgroup of a finite group $ G $. We say that $ H $ satisfies the $ Π$-property in $ G $ if $ | G/K : N_{G/K}((H \cap L)K/K)| $ is a $ π(( H \cap L)K/K ) $-number for any chief factor $ L/K $ of $ G $; and we call that $ H $ satisfies the $ IC $-$ Π$-property in $ G $ if $ H\cap [H, G] $ satisfies the $ Π$-property in $ G $. In this paper, we obtain a criterion of a normal subgroup being contained in the $ p\mathfrak{U} $-hypercenter of a finite group by the $IC$-$ Π$-property of some $ p $-subgroups. |
| title | On the $IC$-$Π$-property of subgroups of finite groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2510.08426 |