# Abelian-extensible automorphism

From Groupprops

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)

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This term is related to: Extensible automorphisms problem

View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

## Definition

### Symbol-free definition

An automorphism of an abelian group is termed **abelian-extensible** if it can be extended to an automorphism for any embedding of the group in an abelian group.

### Definition with symbols

An automorphism of an Abelian group is termed **abelian-extensible** if, for any embedding of as a subgroup of an abelian group , there exists an automorphism of whose restriction to equals .

## Relation with other properties

## Facts

- Divisible abelian group implies every automorphism is abelian-extensible
- Abelian-extensible automorphism not implies power map
- Subgroup of abelian group not implies abelian-extensible automorphism-invariant