1-endomorphism-invariant subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed 1-endomorphism-invariant if, given any defining ingredient::1-endomorphism $$\varphi$$ of $$G$$, $$\varphi(H) \subseteq H$$.

Weaker properties

 * Stronger than::Quasiendomorphism-invariant subgroup
 * Stronger than::Fully characteristic subgroup
 * Stronger than::1-automorphism-invariant subgroup
 * Stronger than::Characteristic subgroup