Interpreting groups and fields in simple, finitary AECs

We prove a version of Hrushovski's 1989 results on almost orthogonal regular types in the context of simple and superstable finitary abstract elementary classes: from a certain expression of 'non-orthogonality' we can conclude the existence of a group acting on the geometry obtained on the set of realizations of a regular Lascar strong type, and if we rule out the presence of a non-classical group we can classify the situation to be one of the classical cases of Hrushovski's theorem.We give two examples of classes of structures in this framework, which clearly demonstrate the phenomena described in the main theorem.