# Normal-potentially relatively 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

A subgroup of a group is termed a **normal-potentially relatively characteristic subgroup** if there exists a group containing such that is a normal subgroup of , and any automorphism of that restricts to an automorphism of also restricts to an automorphism of .

## Relation with other properties

### Stronger properties

- Characteristic subgroup
- Characteristic-potentially characteristic subgroup
- Normal-potentially characteristic subgroup

### Weaker properties

- Normal-extensible automorphism-invariant subgroup
- Normal subgroup
- Potentially relatively characteristic subgroup is a weaker notion, which turns out to be equivalent to normality.
`For full proof, refer: Potentially relatively characteristic equals normal`