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Matematicheskie Zametki, 2022, Volume 111, Issue 1, Pages 8–14
DOI: https://doi.org/10.4213/mzm13229 (Mi mzm13229) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Strong Polynomial Completeness of Almost All Quasigroups

A. V. Galatenko, V. V. Galatenko, A. E. Pankratiev

Lomonosov Moscow State University
Full-text PDF (446 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm13229
Abstract: In the paper, it is proved that almost all quasigroups are strongly polynomially complete, i.e., are not isotopic to quasigroups that are not polynomially complete.
Keywords: quasigroup, isotopy, simplicity, affinity, polynomial completeness.
Funding agency Grant number
Defence Research and Development Organisation (DRDO) SAG/4600/TCID/Prog/QGSEC
This work was financially supported by DRDO (India), the project “Quasigroup Based Cryptography: Security Analysis and Development of Crypto-Primitives and Algorithms (QGSEC)”, grant no. SAG/4600/TCID/Prog/QGSEC.
Received: 19.07.2021
Revised: 21.08.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 1, Pages 7–12
DOI: https://doi.org/10.1134/S0001434622010023
Bibliographic databases:
Document Type: Article
UDC: 512.548.7+519.716.2
Language: Russian
Citation: A. V. Galatenko, V. V. Galatenko, A. E. Pankratiev, “Strong Polynomial Completeness of Almost All Quasigroups”, Mat. Zametki, 111:1 (2022), 8–14; Math. Notes, 111:1 (2022), 7–12
Citation in format AMSBIB
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Linking options:
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  • https://doi.org/10.4213/mzm13229
  • https://www.mathnet.ru/eng/mzm/v111/i1/p8
    • This publication is cited in the following 3 articles:
    1. A. V. Galatenko, V. V. Galatenko, A. E. Pankratiev, “Some properties of almost all n-quasigroups”, jour, 2:4 (2025), 35  crossref
    2. E. E. Gasanov, D. N. Babin, A. V. Galatenko, D. N. Zhuk, G. V. Kalachev, P. A. Panteleev, A. A. Chasovskikh, “MaTIS — shkola V. B. Kudryavtseva: traditsii i razvitie”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2024, no. 6, 15–26  mathnet  crossref  elib
    3. È. È. Gasanov, D. N. Babin, A. V. Galatenko, D. N. Zhuk, G. V. Kalachev, P. A. Panteleev, A. A. Chasovskikh, “MaTIS – the school of V.B. Kudryavtsev: traditions and advancement”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 79:6 (2024), 296–308  mathnet  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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