A classification of finite $p$-groups with a unique $\mathcal{A}_2$-subgroup

TL;DR

This paper classifies finite p-groups with a unique a2-subgroup, solving a problem posed by Berkovich and Janko and providing a comprehensive isomorphism classification.

Contribution

It offers a complete classification of finite p-groups with a unique a2-subgroup, addressing an open problem in the field.

Findings

Complete classification of such p-groups

Resolution of Berkovich and Janko's problem

Identification of isomorphism classes

Abstract

Finite $p$-groups with a unique $\mathcal{A}_2$-subgroup are classified up to isomorphism. A problem proposed by Berkovich and Janko is solved.