Elementary abelian 2-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
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Definition

An elementary abelian 2-group or Boolean group is a group satisfying the following equivalent conditions:

  1. It is isomorphic to the additive group of a vector space over the field of two elements.
  2. It is either the trivial group or is isomorphic to the additive group of a field of characteristic two.
  3. It is a group of exponent at most two.
  4. All the non-identity elements of the group are involutions.

Equivalence of definitions

Further information: Exponent two implies abelian

Relation with other properties

Weaker properties