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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 6, Pages 1295–1313 (Mi izv1519)  

This article is cited in 3 scientific papers (total in 3 papers)

The solvability problem for equations in one unknown in nilpotent groups

N. N. Repin


Abstract: The author constructs a finitely generated nilpotent group of class 3 for which there is no algorithm recognizing the solvability of equations in one unknown. Such an algorithm exists for every finitely generated nilpotent group of class 2. It is proved that for any $c\geqslant10^{20}$ there is no algorithm recognizing the solvability of equations in one unknown in free nilpotent groups of class $c$.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:3, 601–618

Bibliographic databases:

UDC: 512
MSC: Primary 20F10; Secondary 20F18
Received: 18.01.1984

Citation: N. N. Repin, “The solvability problem for equations in one unknown in nilpotent groups”, Izv. Akad. Nauk SSSR Ser. Mat., 48:6 (1984), 1295–1313; Math. USSR-Izv., 25:3 (1985), 601–618

Citation in format AMSBIB
\Bibitem{Rep84}
\by N.~N.~Repin
\paper The solvability problem for equations in one unknown in nilpotent groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 6
\pages 1295--1313
\mathnet{http://mi.mathnet.ru/izv1519}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=772117}
\zmath{https://zbmath.org/?q=an:0583.20027|0565.20018}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 3
\pages 601--618
\crossref{https://doi.org/10.1070/IM1985v025n03ABEH001310}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. K. Burke, “Unification in partially commutative semigroups”, J Automated Reasoning, 12:2 (1994), 209  crossref  mathscinet  zmath
    2. Andrzej Kisielewicz, “Unification in Commutative Semigroups”, Journal of Algebra, 200:1 (1998), 246  crossref
    3. E. I. Timoshenko, “Universal theory of a free polynilpotent group”, Izv. Math., 80:3 (2016), 623–632  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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