Elementary abelian 2-group

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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

• Abelian group
• Elementary abelian group
• Strongly ambivalent group
• Generalized dihedral group
• Rational group
• Ambivalent group