# Normal-potentially fully invariant subgroup

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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 $H$ of a group $G$ is termed a normal-potentially fully invariant subgroup of $G$ if there exists a group $K$ containing $G$ as a normal subgroup, such that $H$ is a fully invariant subgroup of $K$.

## Formalisms

### In terms of the normal-potentially operator

This property is obtained by applying the normal-potentially operator to the property: fully invariant subgroup
View other properties obtained by applying the normal-potentially operator

## Relation with other properties

### Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions