# Abelian-extensible automorphism

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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
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## 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 $\sigma$ of an Abelian group $G$ is termed abelian-extensible if, for any embedding of $G$ as a subgroup of an abelian group $H$, there exists an automorphism $\sigma'$ of $H$ whose restriction to $G$ equals $\sigma$.