Finite-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

Symbol-free definition

An automorphism of a finite group is termed finite-extensible if it extends to an automorphism for every embedding of the finite group inside a finite group.

Relation with other properties

Stronger properties

• Extensible automorphism (of a finite group)
• Inner automorphism (of a finite group)

Weaker properties

• Class-preserving automorphism (of a finite group) For full proof, refer: Finite-extensible implies class-preserving
• Subgroup-conjugating automorphism (of a finite group) For full proof, refer: Finite-extensible implies subgroup-conjugating