Normal subgroups of the full linear group of degree 3 over a distributive lattice (Q1073914)

Let \({\mathcal D}\) be a distributive lattice with 0 and 1, \(GL_ n({\mathcal D})\) the general linear group of degree n over \({\mathcal D}\). The authors describe the normal subgroups of \(GL_ 3({\mathcal D})\) and prove that \(GL_ 3({\mathcal D})\) is solvable. As the authors note an analogous result is not true if \(n\geq 4\).