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Mathematics of the USSR-Izvestiya, 1985, Volume 25, Issue 3, Pages 601–618
DOI: https://doi.org/10.1070/IM1985v025n03ABEH001310 (Mi im1519) 		 
This article is cited in 7 scientific papers (total in 7 papers)

The solvability problem for equations in one unknown in nilpotent groups

N. N. Repin
English version PDF (670 kB) Citations (7)
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DOI: https://doi.org/10.1070/IM1985v025n03ABEH001310
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.
Received: 18.01.1984
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1984, Volume 48, Issue 6, Pages 1295–1313
Bibliographic databases:
UDC: 512
MSC: Primary 20F10; Secondary 20F18
Language: English
Original paper language: Russian
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/im1519}
\mathscinet{http://mathscinet.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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  • https://www.mathnet.ru/eng/im/v48/i6/p1295
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:280
    Russian version PDF:78
    English version PDF:10
    References:44
    First page:1
     
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