# Abelian-extensible endomorphism

From Groupprops

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

## Definition

An endomorphism of an abelian group is termed **abelian-extensible** if, for any group containing , there exists an endomorphism of whose restriction to is .

## 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