# 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:

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