# Rational class-preserving automorphism

## Contents

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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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## 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.