Purely omega-categorical group
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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This article defines a group property obtained by applying the purely operator (viz taking the pure group version) of the following property of groups with additional structure: omega-categorical group
A group is said to be purely omega-categorical if it is countable and is omega-categorical as a pure group. In other words, a group is said to be omega-categorical if it is countable and if its automorphism group has only finitely many oribts in any direct power of the group.