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Algebra and Logic

, Volume 57, Issue 5, pp 327–335 | Cite as

Polynomially Complete Quasigroups of Prime Order

  • A. V. Galatentko
  • A. E. Pankrat’ev
  • S. B. Rodin
Article
  • 6 Downloads

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 results obtained are generalized to n-quasigroups for any n ≥ 3. 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 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • A. V. Galatentko
    • 1
  • A. E. Pankrat’ev
    • 1
  • S. B. Rodin
    • 1
  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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