Congruence subgroup problem for anisotropic groups over semilocal rings (Q1182590)

Let \(K\) be a global field, and let \(G\) be an absolutely almost simple, simply-connected \(K\)-anisotropic algebraic group. The author gives a description of normal subgroups of \(G(R)\) when \(G\) is of types \(A_ 3\), \(B_ n\), \(C_ n\), \(^ 1D_ n\), \(^ 2D_ n\) and some forms of \(^ 2A_ n\), and \(R\) is a semilocal ring in \(K\). This generalizes a result of \textit{G. A. Margulis} [Dokl. Akad. Nauk SSSR 252, 542-546 (1980; Zbl 0503.12011)]. As a corollary, a proof of a conjecture of \textit{V. P. Platonov} [Usp. Mat. Nauk 37, No. 3(225), 3-54 (1982; Zbl 0502.20025)] is obtained for the above groups.