Normal subset

Definition
A subset $$A$$ of a group $$G$$ is termed a normal subset if it satisfies the following equivalent conditions:


 * $$A$$ is a union of defining ingredient::conjugacy classes.
 * For any $$g \in G$$, $$gAg^{-1} \subseteq A$$.
 * For any $$g \in G$$, $$gAg^{-1} = A$$.

A normal subset that is also a subgroup is termed a normal subgroup.