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

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.

Referee's comments incorporated

References in corpus (2)

• Groups in which every non-abelian subgroup is self-centralizing
• Groups in which every non-cyclic subgroup contains its centralizer

Cited by in corpus (3)

• Groups in which every non-abelian subgroup is self-centralizing
• Groups in which every non-abelian subgroup is self-normalized
• Groups in which every non-nilpotent subgroup is self-normalizing