# Weak normal subset-conjugacy-determined subgroup

## Contents

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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.
View other such properties

## 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

### Related subgroup properties

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