Characteristic-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 is a variation of extensible automorphism|Find other variations of extensible automorphism |
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

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