On nearly \({S\Phi}\)-normal subgroups of finite groups
Let \(G\) be a finite group, \(H\) a subgroup of \(G\) and \(H_{sG}\) the subgroup of \(H\) generated by all those subgroups of \(H\) which are \(s\)-permutable in \(G\). Then we say that \(H\) is \(\textit{nearly \(S\Phi\)-normal}\) in \(G\) if \(G\) has a normal subgroup \(T\) such that \(HT\unlhd...
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| Date: | 2024 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2024
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543300721311744 |
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| author | Hussain, M. T. Ullah, S. |
| author_facet | Hussain, M. T. Ullah, S. |
| author_sort | Hussain, M. T. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2024-02-14T18:40:04Z |
| description | Let \(G\) be a finite group, \(H\) a subgroup of \(G\) and \(H_{sG}\) the subgroup of \(H\) generated by all those subgroups of \(H\) which are \(s\)-permutable in \(G\). Then we say that \(H\) is \(\textit{nearly \(S\Phi\)-normal}\) in \(G\) if \(G\) has a normal subgroup \(T\) such that \(HT\unlhd G\) and \(H\cap T\leq \Phi (H)H_{sG}\). In this paper, we study the structure of group \(G\) under the condition that some given subgroups of \(G\) are nearly \(S\Phi\)-normal in \(G\). Some known results are generalised. |
| first_indexed | 2025-12-02T15:26:05Z |
| format | Article |
| id | admjournalluguniveduua-article-2007 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:05Z |
| publishDate | 2024 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-20072024-02-14T18:40:04Z On nearly \({S\Phi}\)-normal subgroups of finite groups Hussain, M. T. Ullah, S. finite group, nearly \(S\Phi\)-normal subgroup, Sylow \(p\)-subgroup, \(p\)-nilpotent group, supersoluble group 20D10; 20D2; 20D35 Let \(G\) be a finite group, \(H\) a subgroup of \(G\) and \(H_{sG}\) the subgroup of \(H\) generated by all those subgroups of \(H\) which are \(s\)-permutable in \(G\). Then we say that \(H\) is \(\textit{nearly \(S\Phi\)-normal}\) in \(G\) if \(G\) has a normal subgroup \(T\) such that \(HT\unlhd G\) and \(H\cap T\leq \Phi (H)H_{sG}\). In this paper, we study the structure of group \(G\) under the condition that some given subgroups of \(G\) are nearly \(S\Phi\)-normal in \(G\). Some known results are generalised. Lugansk National Taras Shevchenko University 2024-02-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007 10.12958/adm2007 Algebra and Discrete Mathematics; Vol 36, No 2 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2007/999 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2007/1145 Copyright (c) 2024 Algebra and Discrete Mathematics |
| spellingShingle | finite group nearly \(S\Phi\)-normal subgroup Sylow \(p\)-subgroup \(p\)-nilpotent group supersoluble group 20D10 20D2 20D35 Hussain, M. T. Ullah, S. On nearly \({S\Phi}\)-normal subgroups of finite groups |
| title | On nearly \({S\Phi}\)-normal subgroups of finite groups |
| title_full | On nearly \({S\Phi}\)-normal subgroups of finite groups |
| title_fullStr | On nearly \({S\Phi}\)-normal subgroups of finite groups |
| title_full_unstemmed | On nearly \({S\Phi}\)-normal subgroups of finite groups |
| title_short | On nearly \({S\Phi}\)-normal subgroups of finite groups |
| title_sort | on nearly \({s\phi}\)-normal subgroups of finite groups |
| topic | finite group nearly \(S\Phi\)-normal subgroup Sylow \(p\)-subgroup \(p\)-nilpotent group supersoluble group 20D10 20D2 20D35 |
| topic_facet | finite group nearly \(S\Phi\)-normal subgroup Sylow \(p\)-subgroup \(p\)-nilpotent group supersoluble group 20D10 20D2 20D35 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007 |
| work_keys_str_mv | AT hussainmt onnearlysphinormalsubgroupsoffinitegroups AT ullahs onnearlysphinormalsubgroupsoffinitegroups |