Groups in which every non-abelian subgroup is self-centralizing

TL;DR

This paper investigates groups where each non-abelian subgroup is self-centralizing, providing classifications for infinite groups and addressing a classification problem for finite p-groups with this property.

Contribution

It characterizes classes of infinite groups with this property and solves a classification problem for finite p-groups, expanding understanding of subgroup-centralizer relationships.

Findings

Classified various infinite groups with the property

Addressed Berkovich's problem on finite p-groups

Identified structural features of groups with self-centralizing non-abelian subgroups

Abstract

We study groups having the property that every non-abelian subgroup contains its centralizer. We describe various classes of infinite groups in this class, and address a problem of Berkovich regarding the classification of finite $p$-groups with the above property.