# Solvable-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

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

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

## Definition

### Symbol-free definition

An automorphism of a solvable group is said to be **solvable-extensible** if it can be extended to an automorphism for any embedding of the given solvable group in a solvable group.

### Definition with symbols

Let be a solvable group and an automorphism of . Then is said to be **solvable-extensible** if for any embedding of , there exists an automorphism of whose restriction to is .

## Relation with other properties=

### Stronger properties

- Extensible automorphism when the underlying group is solvable

### Weaker properties

- Nilpotent-extensible automorphism when the underlying group is nilpotent