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We present results of the electronic and magnetic structure of Mn nanowires adsorbed on Ag(111) and Au(111) surfaces. For finite Mn nanowires on Ag(111) and Au(111) surfaces, our ab initio results show that the large difference between the spin-orbit splitting of these two surfaces leads to completely different magnetic configurations. The magnetic ordering for Mn nanowires adsorbed on Ag(111) is governed by the strong exchange interaction between Mn adatoms. For Mn nano-chains on Au(111), the competition between Heisenberg and Dzyaloshinskii-Moriya interactions leads to a complex magnetic structure of the clusters considered here. Among the more conspicuous results we note a spin-spiral helical type for the nanowire with seven atoms, and a complex magnetic configuration incommensurate with the substrate lattice for a double-sized Mn wire. The effect of the structural relaxation is also investigated …