Allcock, Daniel, 1969-2015-10-022018-01-222015-10-022018-01-222015-05May 2015http://hdl.handle.net/2152/31507textThere are 432 strongly squarefree symmetric bilinear forms of signature (2,1) defined over Z([square root of 2]) whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on Nikulin's) of analysis for the 2-dimensional Weyl chamber to the real quadratic setting, and used it to produce a finite list of quadratic forms which contains all of the ones of interest to us as a sub-list. The standard method for determining whether a hyperbolic reflection group is generated up to finite index by reflections is an algorithm of Vinberg. However, for a large number of our quadratic forms the computation time required by Vinberg's algorithm was too long. We invented some alternatives, which we present here.application/pdfenHyperbolic reflection groupsThesis2015-10-02