On \(S\)-quasinormally embedded subgroups of finite groups
Let \(G\) be a finite group. A subgroup \(A\) is called: 1) \(S\)-quasinormal in \(G\) if \(A\) is permutable with all Sylow subgroups in \(G\) 2) \(S\)-quasinormally embedded in \(G\) if every Sylow subgroup of \(A\) is a Sylow subgroup of some \(S\)-quasinormal subgroup of \(G\). Let \(B_{seG}\)...
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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/689 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543358019698688 |
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| author | Al-Sharo, Kh. A. Shemetkova, Olga Yi, Xiaolan |
| author_facet | Al-Sharo, Kh. A. Shemetkova, Olga Yi, Xiaolan |
| author_sort | Al-Sharo, Kh. A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T09:42:12Z |
| description | Let \(G\) be a finite group. A subgroup \(A\) is called: 1) \(S\)-quasinormal in \(G\) if \(A\) is permutable with all Sylow subgroups in \(G\) 2) \(S\)-quasinormally embedded in \(G\) if every Sylow subgroup of \(A\) is a Sylow subgroup of some \(S\)-quasinormal subgroup of \(G\). Let \(B_{seG}\) be the subgroup generated by all the subgroups of \(B\) which are \(S\)-quasinormally embedded in \(G\). A subgroup \(B\) is called \(SE\)-supplemented in \(G\) if there exists a subgroup \(T\) such that \(G=BT\) and \(B\cap T\le B_{seG}\). The main result of the paper is the following.Theorem. Let \(H\) be a normal subgroup in \(G\), and \(p\) a prime divisor of \(|H|\) such that \((p-1,|H|)=1\). Let \(P\) be a Sylow \(p\)-subgroup in \(H\). Assume that all maximal subgroups in \(P\) are \(SE\)-supplemented in \(G\). Then \(H\) is \(p\)-nilpotent and all its \(G\)-chief \(p\)-factors are cyclic. |
| first_indexed | 2026-02-08T08:01:57Z |
| format | Article |
| id | admjournalluguniveduua-article-689 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:57Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6892018-04-04T09:42:12Z On \(S\)-quasinormally embedded subgroups of finite groups Al-Sharo, Kh. A. Shemetkova, Olga Yi, Xiaolan Finite group, p-nilpotent, S-quasinormal subgroup 20D10, 20D20, 20D25 Let \(G\) be a finite group. A subgroup \(A\) is called: 1) \(S\)-quasinormal in \(G\) if \(A\) is permutable with all Sylow subgroups in \(G\) 2) \(S\)-quasinormally embedded in \(G\) if every Sylow subgroup of \(A\) is a Sylow subgroup of some \(S\)-quasinormal subgroup of \(G\). Let \(B_{seG}\) be the subgroup generated by all the subgroups of \(B\) which are \(S\)-quasinormally embedded in \(G\). A subgroup \(B\) is called \(SE\)-supplemented in \(G\) if there exists a subgroup \(T\) such that \(G=BT\) and \(B\cap T\le B_{seG}\). The main result of the paper is the following.Theorem. Let \(H\) be a normal subgroup in \(G\), and \(p\) a prime divisor of \(|H|\) such that \((p-1,|H|)=1\). Let \(P\) be a Sylow \(p\)-subgroup in \(H\). Assume that all maximal subgroups in \(P\) are \(SE\)-supplemented in \(G\). Then \(H\) is \(p\)-nilpotent and all its \(G\)-chief \(p\)-factors are cyclic. 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/689 Algebra and Discrete Mathematics; Vol 13, No 1 (2012) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/689/pdf Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Finite group p-nilpotent S-quasinormal subgroup 20D10 20D20 20D25 Al-Sharo, Kh. A. Shemetkova, Olga Yi, Xiaolan On \(S\)-quasinormally embedded subgroups of finite groups |
| title | On \(S\)-quasinormally embedded subgroups of finite groups |
| title_full | On \(S\)-quasinormally embedded subgroups of finite groups |
| title_fullStr | On \(S\)-quasinormally embedded subgroups of finite groups |
| title_full_unstemmed | On \(S\)-quasinormally embedded subgroups of finite groups |
| title_short | On \(S\)-quasinormally embedded subgroups of finite groups |
| title_sort | on \(s\)-quasinormally embedded subgroups of finite groups |
| topic | Finite group p-nilpotent S-quasinormal subgroup 20D10 20D20 20D25 |
| topic_facet | Finite group p-nilpotent S-quasinormal subgroup 20D10 20D20 20D25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/689 |
| work_keys_str_mv | AT alsharokha onsquasinormallyembeddedsubgroupsoffinitegroups AT shemetkovaolga onsquasinormallyembeddedsubgroupsoffinitegroups AT yixiaolan onsquasinormallyembeddedsubgroupsoffinitegroups |