# Nilpotent-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)

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

This term is related to: Extensible automorphisms problem

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BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Symbol-free definition

An automorphism of a nilpotent group is said to be **nilpotent-extensible** if it can be extended to an automorphism for every embedding of the given nilpotent group into a nilpotent group.

### Definition with symbols

Let be a nilpotent group and an automorphism of . Then we say that is nilpotent-extensible if for any embedding of in a nilpotent group , there is an automorphism of such that the restriction of to is .

## Relation with other properties

### Stronger properties

- Extensible automorphism when the underlying group is nilpotent
- Solvable-extensible automorphism when the underlying group is nilpotent