# Injective endomorphism-quotient-balanced subgroup

From Groupprops

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

## Relation with other properties

### Stronger properties

- Finite injective endomorphism-invariant subgroup
- Injective endomorphism-invariant subgroup with injective endomorphism-invariant complement

### 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