On some second maximal subgroups of non-solvable groups

Abstract

We call a group $G$ belongs to the class of groups $S_{p}'$, if for every chief factor $A/B$ of $G$, $((A/B)_{p})'=1$. In this paper, some criterions for a group belong to $S_{p}'$ are obtained by using the properties of some second maximal subgroups which related to non-$c_{p}$-normal maximal subgroups.