A note on groups with the minimal conditions for nonabelian and abelian subgroups

TL;DR

This paper provides a new proof of Shunkov's Theorem regarding locally finite groups with minimal conditions for nonabelian subgroups and extends the Suchkova-Shunkov Theorem to Shunkov groups with minimal conditions for abelian subgroups.

Contribution

It offers a novel proof of existing theorems and extends known results to broader classes of groups with minimal subgroup conditions.

Findings

New proof of Shunkov's Theorem for locally finite groups

Extension of Suchkova-Shunkov Theorem to Shunkov groups

Broader understanding of subgroup conditions in group theory

Abstract

We give a new proof of the known Shunkov's Theorem on locally finite groups with the minimal condition for nonabelian subgroups and also an extension of the known Suchkova-Shunkov Theorem on Shunkov groups with the minimal condition for abelian subgroups.