Normal-extensible automorphism-invariant subgroup

Definition
A subgroup of a group is termed a normal-extensible automorphism-invariant subgroup' if it is invariant under every defining ingredient::normal-extensible automorphism of the whole group.

Formalisms
The property of being a normal-extensible automorphism-invariant subgroup can be expressed as the :

Normal-extensible automorphism $$\to$$ Function

It can also be expressed as the endo-invariance property:

Normal-extensible automorphism $$\to$$ Endomorphism

Finally, since the inverse of a normal-extensible automorphism is also normal-extensible, it can be expressed as an auto-invariance property:

Normal-extensible automorphism $$\to$$ Automorphism

Stronger properties

 * Weaker than::Characteristic-extensible automorphism-invariant subgroup
 * Weaker than::Characteristic-potentially characteristic subgroup
 * Weaker than::Normal-potentially characteristic subgroup
 * Weaker than::Normal-potentially relatively characteristic subgroup

Weaker properties

 * Stronger than::Normal subgroup: