Finite elementary abelian group

This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: finite group and elementary abelian group
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Definition

A finite elementary abelian group is a group satisfying the following equivalent conditions:

1. It is both a finite group and an elementary abelian group.
2. It is either a trivial group or the additive group of a finite field.
3. It is the additive group of a finite-dimensional vector space over a finite field.
4. It is either trivial or a direct product of finitely many copies of a group of prime order.

Relation with other properties

Weaker properties

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