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Solvability of Independent Systems of Equations in Finitely Generated Nilpotent Groups

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Abstract

It is proved that the solvability problem for a finite independent system of equations in a finitely generated nilpotent group can effectively be reduced to a similar problem in some finite quotient group of this group. Therefore, this problem is algorithmically solvable. This strengthens a theorem of A. G. Makanin on the residual finiteness and algorithmic solvability of a regular splittable equation in a finitely generated nilpotent group.

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Authors and Affiliations

  1. Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Omsk, 644043, Russia

    V. A. Roman’kov

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  1. V. A. Roman’kov
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Correspondence to V. A. Roman’kov.

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Translated from Matematicheskie Zametki, 2021, Vol. 110, pp. 569–575 https://doi.org/10.4213/mzm12957.

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Roman’kov, V.A. Solvability of Independent Systems of Equations in Finitely Generated Nilpotent Groups. Math Notes 110, 560–564 (2021). https://doi.org/10.1134/S000143462109025X

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  • DOI: https://doi.org/10.1134/S000143462109025X

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