TY - JOUR
AU - Chen, Ruifang
AU - Zhao, Xianhe
AU - Li, Rui
PY - 2021/08/31
Y2 - 2022/01/23
TI - On $\mathcal{M}$-normal embedded subgroups and the structure of finite groups
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 127
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-126034
UR - https://www.mscand.dk/article/view/126034
SP - 243-251
AB - <p>Let $G$ be a group and $H$ be a subgroup of $G$. $H$ is said to be $\mathcal{M}$-normal supplemented in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H_1K<G$ for every maximal subgroup $H_1$ of $H$. Furthermore, $H$ is said to be $\mathcal{M}$-normal embedded in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H\cap K=1$ or $H\cap K$ is $\mathcal{M}$-normal supplemented in $G$. In this paper, some new criteria for a group to be nilpotent and $p$-supersolvable for some prime $p$ are obtained.</p>
ER -