# Homocyclic normal subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): homocyclic group

View a complete list of such conjunctions

## Contents

## Definition

A subgroup of a group is termed a **homocyclic normal subgroup** if it is a normal subgroup of the whole group and is also a homocyclic group as an abstract group. In other words, it is a direct product of pairwise isomorphic cyclic groups.

## Relation with other properties

### Stronger properties

- Cyclic normal subgroup
- Cyclic normal subgroup of finite group
- Homocyclic normal subgroup of finite group