Normal subset of a group

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This article defines a property of subsets of groups
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A subset of a group is termed a normal subset if it satisfies the following equivalent conditions:

  1. It is a union of conjugacy classes.
  2. It equals its conjugate by any element of the group.

This is a generalization, to arbitrary subsets of groups, of the notion of normal subgroup. Specifically, a subgroup is a normal subgroup if and only if it is a normal subset.