2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76150Let f be a nondegenerate quadratic form in at least 5 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 at least 2 or it is 1 and S contains a non-Archimedean valuation, then the S-arithmetic subgroups of the special orthogonal group of 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.An extended version of the paper accepted by the Journal of Number Theory, it includes a self-contained proof of Witt's theorem for local latticesGroup Theorytext