Elementary abelian group:E8

Definition
The elementary abelian group of order eight is defined as followed:


 * It is the defining ingredient::elementary abelian group of order eight.
 * It is the additive group of a three-dimensional vector space over a field of two elements.
 * It is the only abelian group of order eight and exponent two.
 * It is the member of family::generalized dihedral group corresponding to the Klein four-group.
 * It is the member of family::Burnside group $$B(3,2)$$: the free group of rank three and exponent two.

Other descriptions
The group can be defined using GAP's ElementaryAbelianGroup function:

ElementaryAbelianGroup(8)