On Finite Metahamiltonian p-Groups

TL;DR

This paper investigates the properties of finite metahamiltonian p-groups, a class of groups where all non-abelian subgroups are normal, extending the understanding of Hamiltonian group generalizations.

Contribution

It provides new insights into the structure and properties of finite metahamiltonian p-groups, a natural extension of Hamiltonian groups.

Findings

Characterization of finite metahamiltonian p-groups

Conditions under which subgroups are normal

Structural properties of these groups

Abstract

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generalization of Hamiltonian groups. In this paper, the properties of finite metahamiltonian $p$-groups are investigated.