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We have investigated the transport properties of topological insulator based on single-crystal Bi0.83Sb0.17 nanowires. The single-crystal nanowire samples in the diameter range 100 nm – 1.1 μm were prepared by the high frequency liquid phase casting in a glass capillary using an improved Ulitovsky technique; they were cylindrical single-crystals with (1011) orientation along the wire axis. Bi0.83Sb0.17 is a narrow gap semiconductor with energy gap at L point of Brillouin zone ΔE= 21 meV. In accordance with the measurements of the temperature dependence of the resistivity of the samples resistance increases with decreasing temperature, but at low temperatures decrease in the resistance is observed. This effect, decrease in the resistance, is a clear manifestation of the topological insulators properties - the presence on its surface of a highly conducting zone. The Arrhenius plot of R in samples d=1.1 µm and d=200 nm indicates a thermal activation behavior with an activation gap ΔE= 21 and 40 meV, respectively, which proves the presence of the quantum size effect in these samples. We have investigated magnetoresistance of Bi0.83Sb0.17 nanowires at various magnetic field orientations, the cyclotron mass mc and Dingle temperature TD for longitudinal and transverse (B||C3 and B||C2) directions of magnetic fields were determined. The Aharonov-Bohm oscillations of magnetoresistance were observed. The observed effect are discussed.