WNSCC-subgroup

Symbol-free definition
A subgroup of a group is termed a WNSCC-subgroup, or a weak normal subset-conjugacy-closed subgroup, if it is weak normal subset-conjugacy-determined in itself, relative to the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a WNSCC-subgroup or weak normal subset-conjugacy-closed subgroup in $$G$$ if it satisfies the following condition: For any two defining ingredient::normal subsets $$A,B$$ of $$H$$ such that there exists $$g \in G$$ with $$gAg^{-1} = B$$, we have $$A = B$$.

Stronger properties

 * Weaker than::Abnormal subgroup:
 * Weaker than::Direct factor
 * Weaker than::Central factor
 * Weaker than::Retract
 * Weaker than::Subset-conjugacy-closed subgroup
 * Weaker than::Normal subset-conjugacy-closed subgroup

Weaker properties

 * Stronger than::WNSCDIN-subgroup