Geodesic
Polynomially complete quasigroups of prime order
Algebra i logika, Tome 57 (2018) no. 5, pp. 509-521

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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.
Mots-clés : quasigroup, $n$-quasigroup, permutation.
Keywords: Latin square, polynomially complete quasigroup 
@article{AL_2018_57_5_a0,
     author = {A. V. Galatenko and A. E. Pankratiev and S. B. Rodin},
     title = {Polynomially complete quasigroups of prime order},
     journal = {Algebra i logika},
     pages = {509--521},
     publisher = {mathdoc},
     volume = {57},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_5_a0/}
}
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A. V. Galatenko; A. E. Pankratiev; S. B. Rodin. Polynomially complete quasigroups of prime order. Algebra i logika, Tome 57 (2018) no. 5, pp. 509-521. http://geodesic.mathdoc.fr/item/AL_2018_57_5_a0/