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

Proceedings Mathematical Sciences

Long Miao²  Juping Tang¹  Jia Zhang³ 

[1] $$;Wuxi Institute of Technology, Wuxi , People’s Republic of China$$;School of Mathematical Sciences, Yangzhou University, Yangzhou 00, People’s Republic of China$$

关键词: Sylow subgroup;    $mathcal M^ast$-supplemented subgroups;    supersolvable group;    formation.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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 $E leq Z_{mathcal UPhi} (G)$.

【 授权许可】

Unknown