Article
| Title: | A note on the $\Pi $-property of some subgroups of finite groups (English) |
| Author: | Qiu, Zhengtian |
| Author: | Chen, Guiyun |
| Author: | Liu, Jianjun |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 943-953 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies the $\Pi $-property in $G$ if for any chief factor $L / K$ of $G$, $ |G/K : N_{G/K}(HK/K\cap L/K )| $ is a $\pi (HK/K\cap L/K)$-number. 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 $\Pi $-property. (English) |
| Keyword: | finite group |
| Keyword: | $p$-supersoluble group |
| Keyword: | $p$-nilpotent group |
| Keyword: | the $\Pi $-property |
| MSC: | 20D10 |
| MSC: | 20D20 |
| DOI: | 10.21136/CMJ.2024.0226-24 |
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| Date available: | 2024-10-03T12:42:14Z |
| Last updated: | 2024-10-04 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152591 |
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