We solve Gromov's dimension comparison problem on Carnot groups equipped with a Carnot-Carathéodory metric and an adapted Euclidean metric. The proofs use sharp covering theorems relating optimal mutual coverings of Euclidean and Carnot-Carathéodory balls, and elements of sub-Riemannian fractal geometry associated to horizontal self-similar iterated function systems on Carnot groups. To cite this article: Z.M. Balogh et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).
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