Finite elementary abelian group

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.

Weaker properties

 * Stronger than::Homocyclic group of prime power order
 * Stronger than::Abelian group of prime power order
 * Stronger than::Group of prime power order in which all maximal subgroups are automorphic
 * Stronger than::Group of prime power order in which all maximal subgroups are isomorphic