Abelian-extensible endomorphism

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This article defines a function property, viz a property of functions from a group to itself

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 $\alpha$.

Relation with other properties

Stronger properties

• Universal power map for an abelian group. In fact, the universal power maps are precisely the I-endomorphisms for abelian groups. For full proof, refer: Universal power map equals I-endomorphism in variety of abelian groups, Universal power map implies abelian-extensible endomorphism
• Abelian-extensible automorphism