On groups whose subnormal abelian subgroups are normal

TL;DR

This paper investigates groups and Lie algebras where subnormal abelian subgroups or subideals are always normal or ideals, providing detailed classifications for specific classes like hyperabelian groups with periodic Baer radicals.

Contribution

It offers a detailed classification of hyperabelian groups with periodic Baer radicals and hyperabelian Lie algebras with abelian subideals that are ideals, advancing understanding of their structure.

Findings

Classification of hyperabelian groups with periodic Baer radical

Description of hyperabelian Lie algebras with abelian subideals as ideals

Structural insights into groups with subnormal abelian subgroups

Abstract

In the current paper we study the groups, whose subnormal abelian subgroups are normal. We obtained a quite detailed description of such hyperabelian groups with a periodic Baer radical. The description of hyperabelian Lie algebras, whose abelian subideals are ideals, is also obtained.