# Finite-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 a finite group is termed **finite-extensible** if it extends to an automorphism for every embedding of the finite group inside a finite group.

### Definition with symbols

## Formalisms

## Relation with other properties

### Stronger properties

- Extensible automorphism (of a finite group)
- Inner automorphism (of a finite group)

### Weaker properties

- Class-preserving automorphism (of a finite group)
`For full proof, refer: Finite-extensible implies class-preserving` - Subgroup-conjugating automorphism (of a finite group)
`For full proof, refer: Finite-extensible implies subgroup-conjugating`