Elementary abelian 2-group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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An elementary abelian 2-group or Boolean group is a group satisfying the following equivalent conditions:
- It is isomorphic to the additive group of a vector space over the field of two elements.
- It is either the trivial group or is isomorphic to the additive group of a field of characteristic two.
- It is a group of exponent at most two.
- All the non-identity elements of the group are involutions.
Equivalence of definitions
Further information: Exponent two implies abelian