Characteristic-extensible automorphism

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
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.

Stronger properties

 * Extensible automorphism
 * Normal-extensible automorphism