# Normality-preserving endomorphism

From Groupprops

Template:Endomorphism propertyBEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## 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.