Homocyclic group of prime power order

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

Definition

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

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

Relation with other properties

Stronger properties

• Cyclic group of prime power order
• Elementary abelian group

Weaker properties

• Group of prime power order in which all maximal subgroups are isomorphic
• Group of prime power order in which all maximal subgroups are automorphic