Congruence subgroup problem for anisotropic groups over semilocal rings

Abstract

In Chapter I, a theorem of Margulis which gives the structure of normal subgroups ofSL(1,D) for a quaternion division algebraD over a global fieldK of characteristic not 2, is generalized to semi-local ringsR inK. Using this, we obtain in Chapter II, a description of normal subgroups ofG(R) forK-anisotropic algebraic groupsG of typesA 3, Bn, Cn,1Dn,2Dn and some forms of2 A n. As a Corollary, a proof of the Platonov-Margulis conjecture is obtained for the above groups.