Normal subset

This article defines a property of subsets of groups
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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 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.