Elementary abelian group

An elementary abelian group is an abelian group in which the order of every non-identity element is the same. #m/def/group Since this must must be a prime number $𝑝$ , it follows that every elementary abelian group is a $𝑝$ -group, and such groups may be considered a vector space over $ℤ 𝑝$ .

Notation

For a prime $𝑝$ and $ℎ \in ℕ$ , the (unique) elementary abelian group of order $𝑝 ℎ$ is denoted simply by $𝑝 ℎ$ , i.e.

𝑝 ℎ = (ℤ + 𝑝) ℎ

#state/tidy | #lang/en | #SemBr