# Chain-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

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## Definition

### Definition with symbols

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

- A totally 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 .