Potentially characteristic subgroup

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 * 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.