Characteristic-extensible automorphism

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
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Definition

Symbol-free definition

An automorphism of a group is said to be characteristic-extensible if, for every embedding of the group as a characteristic subgroup of a bigger group, the automorphism can be extended to the bigger group.

Definition with symbols

An automorphism $\sigma$ of a group $G$ is said to be characteristic-extensible if for any embedding of $G$ as a characteristic subgroup of a group $H$ , there exists an automorphism $\phi$ of $H$ such that the restriction of $\phi$ to $G$ is $\sigma$ .

Formalisms

In terms of the qualified extensibility operator

This property is obtained by applying the qualified extensibility operator to the property: characteristicity
View other properties obtained by applying the qualified extensibility operator

The property of being a characteristic-extensible automorphism is obtained by applying the qualified extensibility operator, where the automorphism property is the tautology, and the subgroup property is that of being characteristic.

Relation with other properties

Stronger properties

Weaker properties