Elementary abelian group

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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:

Relation with other properties

Stronger properties

  • Cyclic group of prime order viz. simple Abelian group

Weaker properties

Facts

Minimal normal subgroups

Any minimal normal subgroup in a solvable group must be elementary Abelian. This follows by combining the fact that it must be Abelian with the fact that in any group, a minimal normal subgroup is always characteristically simple.