Abelian-extensible endomorphism-invariant subgroup

Definition
A subgroup $$H$$ of an abelian group $$G$$ is termed an abelian-extensible endomorphism-invariant subgroup if it is invariant under all the defining ingredient::abelian-extensible endomorphisms of $$G$$.

Related properties

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