The subgroup structure of linear groups over rings (Q2774187)

Given a Euclidean domain and integers \(1\leq r<n\), the author defines the group \(P_r(n,R)\) to be the subgroup of \(\text{GL}_n(R)\) consisting of matrices of the form \(\left(\begin{smallmatrix} A&0\\ C&B\end{smallmatrix}\right)\) and determines all subgroups \(G\) of \(P_r(n,R)\) containing all matrices of the form \(\left(\begin{smallmatrix} A&0\\ 0&B\end{smallmatrix}\right)\) of determinant \(1\) in terms of an ideal of \(R\) and a subgroup of the group of units in \(R\) when \(n\geq 3\). For \(n=2\) the idea is replaced by additive subgroups of \(R\) invariant under multiplication by units.NEWLINENEWLINENEWLINERemark: There are a few small mistakes but not effecting the result. The result works perfectly over PIDs.