IA-automorphism-balanced subgroup

Definition
A subgroup of a group is termed an IA-automorphism-balanced subgroup or IA-balanced subgroup if every IA-automorphism of the whole group restricts to an IA-automorphism of the subgroup.

Stronger properties

 * Weaker than::IA-automorphism-invariant direct factor
 * Weaker than::Perfect IA-automorphism-invariant subgroup
 * Weaker than::IA-automorphism-invariant subgroup whose commutator subgroup equals its intersection with whole commutator subgroup

Weaker properties

 * Stronger than::Normal subgroup
 * Stronger than::IA-automorphism-invariant subgroup
 * Stronger than::Subgroup with canonical abelianization