# Diagram-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 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

### Definition with symbols

An automorphism of a group is termed **diagram-extensible** if the following holds. Given the following data:

- A partially ordered set with unique minimum element
- A group for each such that
- Inclusions for , compatible with composition

There exist automorphisms of for each such that whenever the restriction of to is , and such that .