• $\mathcal M^\ast$-supplemented subgroups of finite groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/126/02/0187-0197

• # Keywords

Sylow subgroup; M∗-supplemented subgroups; supersolvable group; formation.

• # Abstract

A subgroup $H$ of a group $G$ is said to be $\mathcal M^\ast$-supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G = HK$ and $H \cap K$ is $\mathcal M$-supplemented in $G$. In this paper, we prove as follows: Let $E$ be a normal subgroup of a group $G$. Suppose that every maximal subgroup of every non-cyclic Sylow subgroup $P$ of $F^\ast (E)$ is $\mathcal M^\ast$-supplemented in $G$, then $E \leq Z_{\mathcal U\Phi (G)$.

• # Author Affiliations

1. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, People’s Republic of China
2. Wuxi Institute of Technology, Wuxi 214121, People’s Republic of China

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019