Some conditions for cyclic chief factors of finite groups

Abstract

A subgroup $H$ of a finite group $G$ is called $\scrM$ -supplemented in $G$ if there exists a subgroup $B$ of $G$ such that $G = HB$ and $H_1B$ is a proper subgroup of $G$ for every maximal subgroup $H_1$ of $H$. The main purpose of the paper is to study the influence of $\scrM$ -supplemented subgroups on the cyclic chief factors of finite groups.