Elementary abelian group of prime-fourth order

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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


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).