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
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VIEW 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