Bounded generation of S-arithmetic subgroups of isotropic orthogonal groups over number fields Original Research Article

Let f be a nondegenerate quadratic form in ngreater-or-equal, slanted5 variables over a number field K and let S be a finite set of valuations of K containing all Archimedean ones. We prove that if the Witt index of f is greater-or-equal, slanted2 or it is 1 and S contains a non-Archimedean valuation, then the S-arithmetic subgroups of SOn(f) have bounded generation. These groups provide a series of examples of boundedly generated S-arithmetic groups in isotropic, but not quasi-split, algebraic groups.