$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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Бібліографічні деталі
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

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Резюме:	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.

On \(S\)-quasinormally embedded subgroups of finite groups

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