Injective endomorphism-quotient-balanced subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

A subgroup H of a group G is termed injective endomorphism-quotient-balanced if H is a normal subgroup of G and every injective endomorphism of G sends H to itself and induces an injective endomorphism on the quotient group G/H.

Relation with other properties

Stronger properties

Weaker properties

Metaproperties

Quotient-transitivity

This subgroup property is quotient-transitive: the corresponding quotient property is transitive.
View a complete list of quotient-transitive subgroup properties

Further information: Quotient-balanced implies quotient-transitive

Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself).
View other trim subgroup properties | View other trivially true subgroup properties | View other identity-true subgroup properties