Even-dimensional orthogonal groups as amalgams of unitary groups

This article is part of the program described in [C.D. Bennett, R. Gramlich, C. Hoffman, S. Shpectorov, Curtis–Phan–Tits theory, in: A.A. Ivanov et al. (Eds.), Groups, Combinatorics and Geometry, Proceedings of the Durham Conference on Groups and Geometries, 2001, World Scientific, Singapore, 2003, pp. 13–29]. We provide presentations of even-dimensional orthogonal groups, a characterization of even-dimensional orthogonal groups by certain amalgams of subgroups isomorphic to SU(2,q2), SU(3,q2), and SU(2,q2)×SU(2,q2) over any finite field, and a classification of related amalgams. The results are obtained by diagram geometry, geometric covering theory, and analysis of amalgams.