$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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Видавець:	Lugansk National Taras Shevchenko University
Дата:	2024
Автори:	Hussain, M. T., Ullah, S.
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2024
Теми:	finite group nearly $S\Phi$-normal subgroup Sylow $p$-subgroup $p$-nilpotent group supersoluble group 20D10 20D2 20D35
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2007
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!

Організація

Algebra and Discrete Mathematics

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Резюме:	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.

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

Організація

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