On grouops with formational subnormal or self-normalizing subgroups

TL;DR

This paper investigates the structure of finite groups that have specific subgroups, namely $rak{F}$-subnormal or self-normalizing primary cyclic subgroups, within a particular class of formations that include all nilpotent groups.

Contribution

It characterizes the structure of finite groups with these subgroup properties when the formation $rak{F}$ is subgroup-closed, saturated, and contains all nilpotent groups.

Findings

Provides a detailed structural description of such finite groups.

Extends existing theory to a broader class of formations.

Clarifies the role of $rak{F}$-subnormal and self-normalizing subgroups in group structure.

Abstract

We establish the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups in case $\mathfrak{F}$ is a subgroup-closed saturated superradical formation containing all nilpotent groups.