Normality-preserving endomorphism

Definition
An endomorphism of a group is termed a normality-preserving endomorphism if the image of any normal subgroup of the group under the endomorphism is a normal subgroup of the group.

The term normal endomorphism is also sometimes used for such endomorphisms; however, that term may also be used for an endomorphism that sends each normal subgroup to within itself.

Stronger properties

 * Weaker than::Automorphism
 * Weaker than::Surjective endomorphism