The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
Suppose \(G\) is a finite group and \(H\) is a subgroup of \(G\). \(H\) is said to be \(s\)-permutably embedded in \(G\) if for each prime \(p\) dividing \(|H|\), a Sylow \(p\)-subgroup of \(H\) is also a Sylow \(p\)-subgroup of some \(s\)-permutable subgroup of \(G\); \(H\) is called weakly \(s\)-...
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| Datum: | 2018 |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543355959246848 |
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| author | Li, Changwen |
| author_facet | Li, Changwen |
| author_sort | Li, Changwen |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:28:39Z |
| description | Suppose \(G\) is a finite group and \(H\) is a subgroup of \(G\). \(H\) is said to be \(s\)-permutably embedded in \(G\) if for each prime \(p\) dividing \(|H|\), a Sylow \(p\)-subgroup of \(H\) is also a Sylow \(p\)-subgroup of some \(s\)-permutable subgroup of \(G\); \(H\) is called weakly \(s\)-permutably embedded in \(G\) if there are a subnormal subgroup \(T\) of \(G\) and an \(s\)-permutably embedded subgroup \(H_{se}\) of \(G\) contained in \(H\) such that \(G=HT\) and \(H\cap T\leq H_{se}\). We investigate the influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups. |
| first_indexed | 2026-02-08T07:57:58Z |
| format | Article |
| id | admjournalluguniveduua-article-671 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:58Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6712018-04-04T09:28:39Z The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups Li, Changwen weakly s-permutably embedded subgroups; p-nilpotent; maximal subgroup; 2-maximal subgroup 20D10; 20D20 Suppose \(G\) is a finite group and \(H\) is a subgroup of \(G\). \(H\) is said to be \(s\)-permutably embedded in \(G\) if for each prime \(p\) dividing \(|H|\), a Sylow \(p\)-subgroup of \(H\) is also a Sylow \(p\)-subgroup of some \(s\)-permutable subgroup of \(G\); \(H\) is called weakly \(s\)-permutably embedded in \(G\) if there are a subnormal subgroup \(T\) of \(G\) and an \(s\)-permutably embedded subgroup \(H_{se}\) of \(G\) contained in \(H\) such that \(G=HT\) and \(H\cap T\leq H_{se}\). We investigate the influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671 Algebra and Discrete Mathematics; Vol 12, No 1 (2011) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671/205 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | weakly s-permutably embedded subgroups p-nilpotent maximal subgroup 2-maximal subgroup 20D10 20D20 Li, Changwen The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| title | The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| title_full | The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| title_fullStr | The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| title_full_unstemmed | The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| title_short | The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| title_sort | influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups |
| topic | weakly s-permutably embedded subgroups p-nilpotent maximal subgroup 2-maximal subgroup 20D10 20D20 |
| topic_facet | weakly s-permutably embedded subgroups p-nilpotent maximal subgroup 2-maximal subgroup 20D10 20D20 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/671 |
| work_keys_str_mv | AT lichangwen theinfluenceofweaklyspermutablyembeddedsubgroupsonthepnilpotencyoffinitegroups AT lichangwen influenceofweaklyspermutablyembeddedsubgroupsonthepnilpotencyoffinitegroups |