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

TL;DR

This paper studies the structure of finite groups where non-abelian chief factors are simple and abelian chief factors have automorphism groups in a specific class, exploring their properties and products.

Contribution

It introduces the concept of finite $ca$-$rak F$-groups and analyzes their structure and properties, including permutable products.

Findings

Characterization of finite $ca$-$rak F$-groups

Properties of permutable products of these groups

Structural insights into their chief factors

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 $H/K \leftthreetimes C_G(H/K) \in \mathfrak F$ 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.