Abelian-extensible endomorphism

Definition
An endomorphism $$\alpha$$ of an abelian group $$G$$ is termed abelian-extensible if, for any group $$H$$ containing $$G$$, there exists an endomorphism $$\alpha'$$ of $$H$$ whose restriction to $$G$$ is $$\alpha$$.

Stronger properties

 * Universal power map for an abelian group. In fact, the universal power maps are precisely the I-endomorphisms for abelian groups.
 * Weaker than::Abelian-extensible automorphism