Rational class-preserving automorphism

Definition
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.

Stronger properties

 * Weaker than::Power automorphism
 * Weaker than::Monomial automorphism
 * Weaker than::Inner automorphism
 * Weaker than::Class-preserving automorphism
 * Weaker than::Extended class-preserving automorphism
 * Weaker than::Subgroup-conjugating automorphism

Weaker properties

 * Stronger than::Normal automorphism
 * Stronger than::Weakly normal automorphism