$On nearly ${S\Phi}$-normal subgroups of finite groups$

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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Datum:	2024
Hauptverfasser:	Hussain, M. T., Ullah, S.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Lugansk National Taras Shevchenko University 2024
Schlagworte:	finite group nearly $S\Phi$-normal subgroup Sylow $p$-subgroup $p$-nilpotent group supersoluble group 20D10 20D2 20D35
Online Zugang:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007
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Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-2007
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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
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2024-02-14T18:40:04Z
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	2025-12-02T15:26:05Z
last_indexed	2025-12-02T15:26:05Z
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On nearly \({S\Phi}\)-normal subgroups of finite groups

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