On finite $ca$-$\mathfrak{F}$ groups and their applications

Abstract

Let $\mathfrak{F}$ be a class of groups. A group $G$ is called $ca$-$\mathfrak{F}$-group if its every non-abelian chief factor is simple and $H/K⋋C_G(H/K)\in \mathfrak{F}$ for every abelian chief factor $H/K$ of $G$. In this paper, we investigate the structure of a finite $ca$-$\mathfrak{F}$-group. Properties of mutually permutable products of finite $ca$-$\mathfrak{F}$-groups are studied.