On subgroups in the special linear group over a division algebra that contain the subgroup of diagonal matrices (Q1369599)

Let \(T\) be a division algebra and \(\Gamma=\text{SL}_n(T)\) with \(n\geq 3\). The author proves that, for any subgroup \(H\) of \(\Gamma\) containing all diagonal matrices, there exists a unique \(D\)-net \(\sigma\) such that \(\Gamma(\sigma)\leq H\leq N_\Gamma(\sigma)\) where \(\Gamma(\sigma)\) is the \(D\)-net subgroup corresponding to \(\sigma\).