Normality-preserving endomorphism

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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.

Relation with other properties

Stronger properties

• Automorphism
• Surjective endomorphism