TY - JOUR
ID - 2751
TI - Partially $S$-embedded minimal subgroups of finite groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Zhao, Tao
AU - Zhang, Qingliang
AD - School of Science, Shandong University of Technology
AD - School of Sciences, Nantong University
Y1 - 2013
PY - 2013
VL - 2
IS - 4
SP - 7
EP - 16
KW - s-permutable subgroup
KW - partially S-embedded subgroup
KW - nilpotent group
KW - Formation
DO - 10.22108/ijgt.2013.2751
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_2751.html
L1 - https://ijgt.ui.ac.ir/article_2751_21631b0fa51b75065747f61c434fd5e4.pdf
ER -