Elementary abelian group

An elementary abelian group is an abelian group in which the order of every non-identity element is the same. 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 [[Modular arithmetic| $ℤ 𝑝$ ]].

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.
$𝑝 ℎ = (ℤ + 𝑝) ℎ$

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Elementary abelian group

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