Finite elementary abelian group

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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
View other group property conjunctions OR view all group properties

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