Abelian-quotient-pullbackable automorphism-invariant subgroup

Definition
A subgroup $$H$$ of an abelian group $$G$$ is termed an abelian-quotient-pullbackable automorphism-invariant subgroup if, for every defining ingredient::abelian-quotient-pullbackable automorphism $$\sigma$$ of $$G$$, $$\sigma$$ restricts to an automorphism of $$H$$.

Related properties

 * Abelian-quotient-pullbackable endomorphism-invariant subgroup
 * Abelian-extensible automorphism-invariant subgroup
 * Abelian-extensible endomorphism-invariant subgroup