Elementary abelian group of prime-fourth order

This article is about a family of groups with a parameter that is prime. For any fixed value of the prime, we get a particular group.
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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 $\mathbb {F} _{p}$.

Particular cases

Value of prime number $p$	Value of $p^{4}$	Elementary abelian group of order $p^{4}$
2	16	elementary abelian group:E16
3	81	elementary abelian group:E81
5	625	elementary abelian group:E625

GAP implementation

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