# Intermediately injective endomorphism-invariant 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

### Symbol-free definition

A subgroup of a group is termed **intermediately I-characteristic** if it is an injective endomorphism-invariant subgroup inside every intermediate subgroup.

## Relation with other properties

### Stronger properties

- Isomorph-containing subgroup
- Isomorph-free subgroup
- Homomorph-containing subgroup
- Intermediately fully invariant subgroup