The Classification of Finite Metahamiltonian $p$-Groups

TL;DR

This paper provides a complete classification of finite metahamiltonian p-groups, expanding the understanding of their structure and properties within group theory.

Contribution

It offers the first comprehensive classification of finite metahamiltonian p-groups, a natural extension of Hamiltonian groups.

Findings

Finite metahamiltonian p-groups are fully classified.

Non-abelian subgroups of these groups are always normal.

The classification clarifies the structure of these groups.

Abstract

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generation of Hamiltonian groups. In this paper, a complete classification of finite metahamiltonian $p$-groups is given.