Properly discontinuous groups of affine transformations with orthogonal linear part

Abels H, Margulis GA, Soifer GA. Groupes proprement discontinus de transformations affines avec parties linéaires orthogonales. Comptes rendus de l'Académie des sciences. Série 1, Mathématique . 1997;324(3):253-258.Let Gamma be a subgroup of the group of all affine transformations of a real affine space A of finite dimension. Suppose that Gamma acts properly discontinuously on A. We determine which orthogonal groups can occur as Zariski closures of the linear part of Gamma. Our methods yield a proof of Auslander's conjecture for affine spaces of dimension at most 6