Socle of Hamiltonian Group

TL;DR

This paper explicitly determines the socle of a Hamiltonian group, which is generated by all minimal normal subgroups, providing a clear structural insight into these groups.

Contribution

The paper offers a precise characterization of the socle in Hamiltonian groups, a specific class of groups where all subgroups are normal.

Findings

Explicit description of the socle in Hamiltonian groups

Structural insights into minimal normal subgroups

Clarification of the subgroup generated by these minimal normal subgroups

Abstract

The socle of a group $G$ is the subgroup generated by all minimal normal subgroups of $G$. In this short note, we determine the socle of a Hamiltonian group explicitly.