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We study effects of Gribov copies in the Maximal Abelian gauge in lattice gluodynamics. We confirm earlier results that with effective gauge fixing algorithm one finds Gribov copies of the maximal Abelian gauge which produce about 90% of the nonabelian string tension after Abelian projection. At the same time using much less effective relaxation algorithm one finds Gribov copies with nice Abelian dominance for the string tension.

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