# 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.
View other such prime-parametrized groups

## 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).