3-abelian group

Definition
A group is termed 3-abelian if it is n-abelian for $$n = 3$$, i.e., the cube map is an endomorphism of the group.

Facts

 * Levi's characterization of 3-abelian groups
 * Cube map is endomorphism implies class three
 * Cube map is surjective endomorphism implies abelian
 * Cube map is endomorphism iff abelian (if order is not a multiple of 3)

For more on power maps being endomorphisms, see n-abelian group.