Chain-extensible automorphism

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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)
View other automorphism properties OR View other function properties

This term is related to: Extensible automorphisms problem
View other terms related to Extensible automorphisms problem | View facts related to Extensible automorphisms problem

Definition

Definition with symbols

An automorphism $\sigma$ of a group $G$ is termed chain-extensible if the following holds. Given the following data:

A totally ordered set $I$ with unique minimum element $0$
A group $G_{i}$ for each $i\in I$ such that $G_{0}=G$
Inclusions $G_{i}\to G_{j}$ for $i<j$ , compatible with composition

There exist automorphisms $\sigma _{i}$ of $G_{i}$ for each $i$ such that whenever $i<j$ the restriction of $\sigma _{j}$ to $G_{i}$ is $\sigma _{i}$ , and such that $\sigma _{0}=\sigma$ .

Relation with other properties

Stronger properties

Weaker properties