Locally finite classical Tits chamber systems of large order (Q1085275)

This paper is one of the major steps in classifying locally finite Tits chamber systems of classical type. The paper is devoted to the ones which are of large order. The main theorem is that if one has a locally finite Tits chamber system with hyperbolic diagram and transitive automorphism group with finite chamber stabilizer, then with a few exceptions one also has a parabolic system. After having this theorem then one is able to use group theory (for example the amalgam method) to get the structure of the parabolics and then information about the original chamber system. As an application of this the author proves that if the order is sufficiently large (i.e. \(| \Delta_ i(c)| \geq 6\), for any chamber c), then with a few exceptions the chamber system is the chamber system of a building. This will be done by using the above result and then a result due to \textit{R. Niles} [J. Algebra 75, 484-494 (1982; Zbl 0491.20020)] saying that the parabolic systems in question belong to groups of Lie type.