On Some Results in the Theory of Finite Partially Soluble Groups

Abstract

This article provides an overview of some recent results and ideas related to the study of finite groups depending on the restrictions on some systems of their sections. In particular, we discuss some properties of the lattice of all subgroups of a finite group related with conditions of permutability and generalized subnormality for subgroups. The paper contains more than 30 open problems which were posed, at different times, by some mathematicians working in the discussed direction.

Keywords

Finite group / Subgroup lattice / G-covering subgroup system / $\Pi $-subnormal subgroup')">$\Pi $-subnormal subgroup / $\sigma $-nilpotent group')">$\sigma $-nilpotent group