The research of discontinuous groups with respect to different geometries has made considerable progress (cf. references). One can state the remarkable fact that conditions which all characterize the same discontinuous motion groups in Euclidean spaces of the same finite dimension define different classes of discontinuous transformation groups in other geometries. Moreover in the earlier paper [15], eight conditions are described which define different classes of generalized discontinuous motion groups in metric spaces, in particular in Euclidean spaces of arbitrary dimension. The increase in models in the Euclidean plane geometry is given in the paper [18]. Now, we will give all classes of weak discontinuous or so-called D' 3-discontinuous motion groups of the Euclidean space.
