# Homocyclic normal subgroup of finite group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: homocyclic normal subgroup with a group property imposed on theambient group: finite group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Contents

## Definition

A subgroup of a group is termed a **homocyclic normal subgroup** if it is a homocyclic normal subgroup (i.e., a homocyclic group and a normal subgroup) and the whole group is a finite group.