Elementary abelian group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
Definition
Symbol-free definition
An elementary Abelian group is a group that satisfies the following equivalent conditions:
- It is an Abelian characteristically simple group
- It is a direct product of isomorphic subgroups, each being cyclic of prime order
- It is the additive group of a vector space over a prime field
Relation with other properties
Stronger properties
- Cyclic group of prime order viz. simple Abelian group