Normal subgroups of classical groups over rings (Q1909736)

The normal subgroup problem for a classical group \(G\) over a ring \(R\) is to study whether the ``sandwich theorem'' holds, i.e., for any subgroup \(H\) of \(G\) normalized by the elementary subgroup of \(G\), there is a unique ideal \(J\) of \(R\), such that \(H\) lies between the general and elementary congruence subgroups with respect to \(J\). The authors prove that, for the pseudo-orthogonal groups over a wide class of rings, containing every ring which is finitely generated as a module over its center, the normal subgroup problem has a positive solution. It covers many previous relevant results.