Potentially characteristic subgroup

You might be looking for:

• normal equals potentially characteristic: A normal subgroup $H$ of a group $G$ is potentially characteristic: there exists a group $K$ containing $G$ such that $H$ is a characteristic subgroup of $K$.
• group property-conditionally potentially characteristic subgroup: This is the notion of being potentially characteristic with respect to a group property.
• potentially characteristic subgroups characterization problem
• potentially operator: This takes as input a subgroup property and outputs the property of being a subgroup that can satisfy the property in some ambient group.