Finite groups in which generalized normality is a transitive relation

TL;DR

This paper explores the properties of finite groups where generalized normality is transitive, discussing known results and open problems in the context of $\sigma$-properties and generalized T-groups.

Contribution

It provides new insights into the structure of finite groups with transitive generalized normality and addresses open problems in the theory of $\sigma$-properties.

Findings

Analysis of conditions for transitivity of generalized normality

Identification of open problems in $\sigma$-properties

Connections between generalized T-groups and normality transitivity

Abstract

In this paper, we discuss some well-known results and some open problems of the theory of $\sigma$-properties of a group related to the study of generalized $T$-groups.