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Algebra i logika, 2018, Volume 57, Number 5, Pages 509–521
DOI: https://doi.org/10.33048/alglog.2018.57.501 (Mi al863) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Polynomially complete quasigroups of prime order

A. V. Galatenko, A. E. Pankratiev, S. B. Rodin

Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
Full-text PDF (175 kB) Citations (6)
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DOI: https://doi.org/10.33048/alglog.2018.57.501
Abstract: We formulate a polynomial completeness criterion for quasigroups of prime order, and show that verification of polynomial completeness may require time polynomial in order. The obtained results are generalized to $n$-quasigroups for any $n\ge3$. In conclusion, simple corollaries are given on the share of polynomially complete quasigroups among all quasigroups, and on the cycle structure of row and column permutations in Cayley tables for quasigroups that are not polynomially complete.
Keywords: quasigroup, Latin square, polynomially complete quasigroup, $n$-quasigroup, permutation.
Funding agency Grant number
Russian Foundation for Basic Research 15-51-45031
Supported by RFBR and by Department of Science and Technology of Government of India, project No. 15-51-45031.
Received: 05.05.2017
English version:
Algebra and Logic, 2018, Volume 57, Issue 5, Pages 327–3335
DOI: https://doi.org/10.1007/s10469-018-9505-6
Bibliographic databases:
Document Type: Article
UDC: 512.548.7+519.716.2
Language: Russian
Citation: A. V. Galatenko, A. E. Pankratiev, S. B. Rodin, “Polynomially complete quasigroups of prime order”, Algebra Logika, 57:5 (2018), 509–521; Algebra and Logic, 57:5 (2018), 327–3335
Citation in format AMSBIB
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\paper Polynomially complete quasigroups of prime order
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\vol 57
\issue 5
\pages 509--521
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\crossref{https://doi.org/10.33048/alglog.2018.57.501}
\transl
\jour Algebra and Logic
\yr 2018
\vol 57
\issue 5
\pages 327--3335
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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