Weak subset-conjugacy-determined subgroup

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 $H\leq K\leq G$ are groups. We say that $H$ is a weak subset-conjugacy-determined subgroup in $K$ if any two subsets of $H$ that are conjugate in $G$ are conjugate in $K$.

Relation with other properties

Stronger properties

• Subset-conjugacy-determined subgroup

Weaker properties

• Weak normal subset-conjugacy-determined subgroup