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Matematicheskie Zametki, 2021, Volume 110, Issue 4, Pages 569–575
DOI: https://doi.org/10.4213/mzm12957 (Mi mzm12957) 		 
Solvability of Independent Systems of Equations in Finitely Generated Nilpotent Groups

V. A. Roman'kov

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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DOI: https://doi.org/10.4213/mzm12957
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.
Keywords: Diophantine problem, nilpotent group, regular equation, independent system, residual finiteness.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences 0314-2019-0004
This work was supported by the Program of Basic Scientific Researches of the Siberian Division of Russian Academy of Sciences I.1.1.4 (grant no. 0314-2019-0004).
Received: 13.11.2020
Revised: 09.06.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 4, Pages 560–564
DOI: https://doi.org/10.1134/S000143462109025X
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: Russian
Citation: V. A. Roman'kov, “Solvability of Independent Systems of Equations in Finitely Generated Nilpotent Groups”, Mat. Zametki, 110:4 (2021), 569–575; Math. Notes, 110:4 (2021), 560–564
Citation in format AMSBIB
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