# Group in which every element is order-automorphic

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## Definition

A **group in which every element is order-automorphic** is a group such that, whenever two elements have the same order, there is an automorphism of the group sending the first element to the second element.

## Relation with other properties

### Stronger properties

- Group whose automorphism group is transitive on non-identity elements
- Group in which every element is order-conjugate