Sobolev Mappings and Moduli Inequalities on Carnot Groups

. We study the mappings that satisfy moduli inequalities on Carnot groups. We prove that the homeomorphisms satisfying the moduli inequalities ( Q -homeomorphisms) with a locally integrable function Q are Sobolev mappings. On this base in the frameworks of the weak inverse mapping theorem, we prove that, on the Carnot groups G ; the mappings inverse to Sobolev homeomorphisms of finite distortion of the class W v , loc 1 Ω Ω ′ belong to the Sobolev class W 1 , loc 1 Ω ′ Ω .