$On $S$-quasinormally embedded subgroups of finite groups$

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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Дата:	2018
Автори:	Al-Sharo, Kh. A., Shemetkova, Olga, Yi, Xiaolan
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2018
Теми:	Finite group p-nilpotent S-quasinormal subgroup 20D10 20D20 20D25
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/689
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-689
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua: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
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T09:42:12Z
collection	OJS
language	English
topic	Finite group p-nilpotent S-quasinormal subgroup 20D10 20D20 20D25
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
topic_facet	Finite group p-nilpotent S-quasinormal subgroup 20D10 20D20 20D25
format	Article
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.
title	On $S$-quasinormally embedded subgroups of finite groups
title_short	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_sort	on $s$-quasinormally embedded subgroups of finite groups
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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
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
first_indexed	2025-07-17T10:36:30Z
last_indexed	2025-07-17T10:36:30Z
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On \(S\)-quasinormally embedded subgroups of finite groups

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