Characteristic subset of a group

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

  1. For any automorphism \sigma of G, \sigma(A) \subseteq A, i.e., \sigma(a) \in A for all a \in A.
  2. For any automorphism \sigma of G, \sigma(A) = A.
  3. For any automorphism \sigma of G, the restriction of \sigma to A is a bijection from A to itself.