# Homocyclic group of prime power order

From Groupprops

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: homocyclic group and group of prime power order

View other group property conjunctions OR view all group properties

## Contents

## Definition

A **homocyclic group of prime power order** is a group satisfying the following two equivalent conditions:

- It is the direct product of finitely many isomorphic cyclic groups, each of prime power order.
- It is a group of prime power order that is also a homocyclic group.