On general linear groups over exchange rings

Let R be an exchange ring. We prove that the relative elementary subgroups En(R, I) are normal in the general linear group GLn(R) if n = 1 and that the standard commutator formula En(R, I) = [En(R), En(R, I)] = [En(R), Cn(R, I)] holds if n = 3. Moreover, we classify the subgroups of GLn(R) that are normalized by the elementary subgroup En(R) in the case n >= 3.