Homocyclic group of prime power order

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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

Weaker properties