Elementary abelian group of prime-fourth order

Definition
Let $$p$$ be a prime number. This group, denoted $$E_{p^4}$$ or $$(\mathbb{Z}_p)^4$$, is defined as the elementary abelian group of order $$p^4$$. Equivalently, it can be defined in the following equivalent ways:


 * 1) It is the external direct product of four copies of the group of prime order.
 * 2) It is the additive group of the four-dimensional vector space over the field $$\mathbb{F}_p$$.

GAP implementation
The group can be constructed using the ElementaryAbelianGroup function as ElementaryAbelianGroup(p^4).