# Fixed-class extensible automorphism

From Groupprops

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)

View other automorphism properties OR View other function properties

This is a variation of extensible automorphism|Find other variations of extensible automorphism |

*This is the property of being a variety-extensible automorphism for the following variety of algebras:* fixed-class nilpotent groups

## Contents

## Definition

### Definition with symbols

Let be a nilpotent group and let be the nilpotence class of . An automorphism of is said to be **fixed-class extensible** if, for any embedding in a group of nilpotence class , there exists an automorphism of such that the restriction of to is .

## Relation with other properties

### Weaker properties

- Finitely fixed-class extensible automorphism for a finite group
- Fixed-class extensible endomorphism