IA-automorphism-invariant subgroup

Definition
A subgroup of a group is termed an IA-automorphism-invariant subgroup if it is invariant under all IA-automorphisms of the whole group.

Formalisms
The property of being an IA-automorphism-invariant subgroup is the with respect to IA-automorphisms, and has the function restriction expression:

Left side of function restriction expression::IA-automorphism $$\to$$ Function

In particular, it is an endo-invariance property with function restriction expression:

IA-automorphism $$\to$$ Right side of function restriction expression::Endomorphism

In fact, since inverses of IA-automorphisms are IA-automorphisms, it is an auto-invariance property with function restriction expression:

IA-automorphism $$\to$$ Right side of function restriction expression::Automorphism

Stronger properties

 * Weaker than::Characteristic subgroup
 * Weaker than::IA-balanced subgroup

Weaker properties

 * Stronger than::Normal subgroup