Groups with the Minimal Conditions for Subgroups and for Nonabelian Subgroups

TL;DR

This paper characterizes groups satisfying minimal conditions for subgroups and nonabelian subgroups within broad classes, showing they are Chernikov groups, thus linking subgroup conditions to a well-known group class.

Contribution

It establishes a characterization of groups with minimal conditions for subgroups and nonabelian subgroups as Chernikov groups within certain broad classes.

Findings

Groups in classes al D and al B satisfy the minimal condition iff they are Chernikov.

Provides a unifying criterion linking subgroup conditions to Chernikov groups.

Extends known results to wider classes of groups.

Abstract

For some very wide classes $\mathfrak{D}$ and $\mathfrak{B}\subset\mathfrak{D}$ of groups, the author proves that an arbitrary (nonabelian) group $G\in \mathfrak{D}$ (respectively $G\in \mathfrak{B}$) satisfies the minimal condition for (nonabelian) subgroups iff it is Chernikov