HEP-subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a HEP-subgroup or is said to have the Homomorphism Extension Property if, for any homomorphism of groups $$\varphi:H \to G$$, there exists an endomorphism $$\varphi'$$ of $$G$$ such that the restriction of $$\varphi'$$ to $$H$$ equals $$\varphi$$.

Stronger properties

 * Weaker than::Homomorphism-closed subgroup
 * Weaker than::Direct factor
 * Weaker than::Retract

Weaker properties

 * Stronger than::EEP-subgroup