# Extensible partial automorphism

From Groupprops

Template:Partial function property

This term is related to: Extensible automorphisms problem

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

## Contents

## Definition

### Symbol-free definition

A partial automorphism of a group is said to be **extensible** if it is a partial automorphism for any bigger group containing that group. In other words, for any bigger group containing the group, the given partial function can be realized as the restriction of an automorphism on the *bigger group*.

## Relation with other properties

### Stronger properties

- Partial inner automorphism
- Partial extensible automorphism: Any partial automorphism obtained by restricting an extensible automorphism, is an extensible partial automorphism