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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 491, Pages 5–10
DOI: https://doi.org/10.31857/S2686954320020022 (Mi danma43) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Construction of infinite finitely presented nilsemigroup

A. Ya. Belovab, I. A. Ivanov-Pogodaevc

a Shenzhen University, Shenzhen, China
b Bar-Ilan University, Ramat-Gan, Israel
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320020022
Abstract: An infinite finitely presented nilsemigroup with identity $x^9$ = 0 is constructed. This construction answers the question of L.N. Shevrin and M.V. Sapir. The proof is based on the construction of a sequence of geometric complexes, each obtained by gluing several simple 4-cycles (squares). These complexes have certain geometric and combinatorial properties. Actually, the semigroup is the set of word codings of paths on such complexes. Each word codes a path on some complex. Defining relations correspond to pairs of equivalent short paths. The shortest paths in terms of the natural metric are associated with nonzero words in the subgroup. Codings that are not presented by some path or presented by non-shortest paths can be reduced to a zero word.
Keywords: finitely presented semigroups, Burnside-type problems.
Funding agency Grant number
Russian Science Foundation 17-11-01377
Contest «Young Russian Mathematics»
This work was supported by the Russian Science Foundation, grant no. 17-11-01377. The second author is the winner of the contest “Young Russian Mathematics”.
Presented: A. L. Semenov
Received: 27.11.2019
Revised: 27.11.2019
Accepted: 23.01.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 2, Pages 81–85
DOI: https://doi.org/10.1134/S1064562420020027
Bibliographic databases:
Document Type: Article
UDC: 512.53
Language: Russian
Citation: A. Ya. Belov, I. A. Ivanov-Pogodaev, “Construction of infinite finitely presented nilsemigroup”, Dokl. RAN. Math. Inf. Proc. Upr., 491 (2020), 5–10; Dokl. Math., 101:2 (2020), 81–85
Citation in format AMSBIB
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\by A.~Ya.~Belov, I.~A.~Ivanov-Pogodaev
\paper Construction of infinite finitely presented nilsemigroup
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 491
\pages 5--10
\mathnet{http://mi.mathnet.ru/danma43}
\crossref{https://doi.org/10.31857/S2686954320020022}
\zmath{https://zbmath.org/?q=an:07424559}
\elib{https://elibrary.ru/item.asp?id=42860651}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 2
\pages 81--85
\crossref{https://doi.org/10.1134/S1064562420020027}
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    • This publication is cited in the following 1 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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