University of IsfahanInternational Journal of Group Theory2251-76502420131201Partially $S$-embedded minimal subgroups of finite groups716275110.22108/ijgt.2013.2751ENTaoZhaoSchool of Science, Shandong University of TechnologyQingliangZhangSchool of Sciences, Nantong UniversityJournal Article20130213Suppose 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.https://ijgt.ui.ac.ir/article_2751_21631b0fa51b75065747f61c434fd5e4.pdf