Group in which every element is order-automorphic

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

Weaker properties

• Group in which any two elements generating the same cyclic subgroup are automorphic
• Group in which every element is automorphic to its inverse