SCDIN-subgroup

Symbol-free definition
A subgroup of a group is termed a SCDIN-subgroup, or subset-conjugacy-determined in normalizer, if it is a defining ingredient::subset-conjugacy-determined subgroup inside its defining ingredient::normalizer, relative to the whole group.

Definition
A subgroup $$H$$ of a group $$G$$ is termed a SCDIN-subgroup, or subset-conjugacy-determined in normalizer, if, whenever $$A,B$$ are subsets of $$H$$ such that there exists $$g \in G$$ with $$gAg^{-1} =B$$, there exists $$k \in N_G(H)$$ such that $$kak^{-1} = gag^{-1}$$ for all $$a in A$$.