# Weakly image-closed characteristic 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

### Definition with symbols

A subgroup of a group is termed a **weakly image-closed characteristic subgroup** of if, for any normal subgroup of contained in , the quotient group is a characteristic subgroup of the quotient group .

## Formalisms

### In terms of the weak image condition operator

This property is obtained by applying the weak image condition operator to the property: characteristic subgroup

View other properties obtained by applying the weak image condition operator

## Relation with other properties

### Stronger properties

- Image-closed characteristic subgroup
- Weakly image-closed fully invariant subgroup
- Image-closed fully invariant subgroup
- Quotient-subisomorph-containing subgroup
- Verbal subgroup