# Semi-strongly image-potentially 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]

This term is related to: NIPC conjecture

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## Definition

A subgroup of a group is termed a **semi-strongly image-potentially characteristic subgroup** if there exists a group with a surjective homomorphism such that is a characteristic subgroup of .

## Relation with other properties

### Stronger properties

- Characteristic subgroup
- Kernel of a characteristic action on an abelian group
- Strongly image-potentially characteristic subgroup