Topological properties of mappings with finite distortion on Carnot groups

We prove that every mapping with finite distortion on a Carnot group is open and discrete provided that it is quasilight and the distortion coefficient is integrable. Also, we estimate the Hausdorff dimension of the preimages of points for mappings on a Carnot group with a bounded multiplicity function and summable distortion coefficient. Furthermore, we give some example showing that the obtained estimates cannot be improved.