Rational class-preserving automorphism

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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An automorphism \sigma of a group G is termed a rational class-preserving automorphism if it satisfies the following equivalent conditions:

  • For any g \in G, there exists h \in G such that \langle \sigma(g) \rangle and \langle hgh^{-1} \rangle are equal.
  • \sigma sends every cyclic subgroup to a conjugate subgroup.

Relation with other properties

Stronger properties

Weaker properties