Weak normal subset-conjugacy-determined 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 if weak normal subset-conjugacy-determined in K relative to G if, for any normal subsets A,B \subseteq H such that there exists g \in G with gAg^{-1} = B, there exists k \in K such that kAk^{-1} = B.

The modifier weak here denotes that g and k may not have the same element-wise action on A.

Relation with other properties

Stronger properties

Related subgroup properties

  • WNSCDIN-subgroup: A subgroup that is weak normal subset-conjugacy-determined inside its normalizer.