# Group property-conditionally characteristic-potentially characteristic subgroup

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This term is related to: potentially characteristic subgroups characterization problem

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## Definition

Let be a subgroup of a group , and be a group property. We say that is **normal-potentially characteristic** in relative to if there exists a group containing and satisfying such that and are both characteristic subgroups of .

If we simply use the term normal-potentially characteristic subgroup, it means that is taken to be the tautology -- the property satisfied by all groups.