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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Видавець: | Lugansk National Taras Shevchenko University |
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Дата: | 2024 |
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Lugansk National Taras Shevchenko University
2024
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Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007 |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
institution |
Algebra and Discrete Mathematics |
collection |
OJS |
language |
English |
topic |
finite group nearly \(S\Phi\)-normal subgroup Sylow \(p\)-subgroup \(p\)-nilpotent group supersoluble group 20D10 20D2 20D35 |
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 |
topic_facet |
finite group nearly \(S\Phi\)-normal subgroup Sylow \(p\)-subgroup \(p\)-nilpotent group supersoluble group 20D10 20D2 20D35 |
format |
Article |
author |
Hussain, M. T. Ullah, S. |
author_facet |
Hussain, M. T. Ullah, S. |
author_sort |
Hussain, M. T. |
title |
On nearly \({S\Phi}\)-normal subgroups of finite groups |
title_short |
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_sort |
on nearly \({s\phi}\)-normal subgroups of finite groups |
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. |
publisher |
Lugansk National Taras Shevchenko University |
publishDate |
2024 |
url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007 |
work_keys_str_mv |
AT hussainmt onnearlysphinormalsubgroupsoffinitegroups AT ullahs onnearlysphinormalsubgroupsoffinitegroups |
first_indexed |
2024-04-12T06:13:54Z |
last_indexed |
2024-04-12T06:13:54Z |
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