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 $pd$-chief factor $A/B$ of $G$, $((A/B)_{p})'=1$. In this paper, we investigate the influence of some second maximal subgroups which are related to non-$c_{p}$-normal maximal subgroups on the structure of $S_{p}'$.

Keywords

• second maximal subgroups
• maximal subgroups
• simple groups
• non-solvable groups
• $c_{p}$-normal.

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