Group theory MOC

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 , it follows that every elementary abelian group is a p-group, and such groups may be considered a vector space over [[Modular arithmetic|]].

Notation

For a prime and , the (unique) elementary abelian group of order is denoted simply by , i.e.

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