Geodesic
Solvability of Independent Systems of Equations in Finitely Generated Nilpotent Groups
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 569-575

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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.
Mots-clés : Diophantine problem
Keywords: nilpotent group, regular equation, independent system, residual finiteness. 
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     author = {V. A. Roman'kov},
     title = {Solvability of {Independent} {Systems} of {Equations} in {Finitely} {Generated} {Nilpotent} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {569--575},
     publisher = {mathdoc},
     volume = {110},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a6/}
}
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V. A. Roman'kov. Solvability of Independent Systems of Equations in Finitely Generated Nilpotent Groups. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 569-575. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a6/