Elementary abelian 2-group

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 defining ingredient::involutions.

Weaker properties

 * Stronger than::Abelian group
 * Stronger than::Elementary abelian group
 * Stronger than::Strongly ambivalent group
 * Stronger than::Generalized dihedral group
 * Stronger than::Rational group
 * Stronger than::Ambivalent group