@article {
author = {Zhao, Tao and Zhang, Qingliang},
title = {Partially $S$-embedded minimal subgroups of finite groups},
journal = {International Journal of Group Theory},
volume = {2},
number = {4},
pages = {7-16},
year = {2013},
publisher = {University of Isfahan},
issn = {2251-7650},
eissn = {2251-7669},
doi = {10.22108/ijgt.2013.2751},
abstract = {Suppose that $H$ is a subgroup of $G$, then $H$ is said to be $s$-permutable in $G$, if $H$ permutes with every Sylow subgroup of $G$. If $HP=PH$ hold for every Sylow subgroup $P$ of $G$ with $(|P|, |H|)=1$), then $H$ is called an $s$-semipermutable subgroup of $G$. In this paper, we say that $H$ is partially $S$-embedded in $G$ if $G$ has a normal subgroup $T$ such that $HT$ is $s$-permutable in $G$ and $H\cap T\leq H_{\overline{s}G}$, where $H_{\overline{s}G}$ is generated by all $s$-semipermutable subgroups of $G$ contained in $H$. We investigate the influence of some partially $S$-embedded minimal subgroups on the nilpotency and supersolubility of a finite group $G$. A series of known results in the literature are unified and generalized.},
keywords = {s-permutable subgroup,partially S-embedded subgroup,nilpotent group,Formation},
url = {https://ijgt.ui.ac.ir/article_2751.html},
eprint = {https://ijgt.ui.ac.ir/article_2751_21631b0fa51b75065747f61c434fd5e4.pdf}
}