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.

中文翻译：

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卡诺群上有限畸变映射的拓扑性质

我们证明卡诺群上的每个具有有限畸变的映射都是开离散的，只要它是准光的并且畸变系数是可积的。此外，我们还利用有界多重函数和可求和失真系数来估计卡诺群上映射的点原像的豪斯多夫维数。此外，我们给出了一些例子，表明所获得的估计无法改进。