Elementary Abelian Group

In group theory, an elementary abelian group is a finite abelian group, where every nontrivial element has order p, where p is a prime; in particular it is a p-group.

By the classification of finitely generated abelian groups, every elementary abelian group must be of the form

(Z/pZ)n

for n a non-negative integer (sometimes called the group's rank). Here, Z/pZ denotes the cyclic group of order p (or equivalently the integers mod p), and the notation means the n-fold Cartesian product.