Conjugation-invariantly relatively normal subgroup

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This article describes a property that can be evaluated for a triple of a group, a subgroup of the group, and a subgroup of that subgroup.
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Definition

Suppose H \le K \le G. We say that H is conjugation-invariantly relatively normal in K with respect to G if H is a normal subgroup in every conjugate of K in G that contains H.

Relation with other properties

Stronger properties

Weaker properties