Geodesic
Quasigroups and their applications
Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 111-122

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A survey of results obtained within the project 0AAAA-A16-116070810025-5 and the recent joint project with Indian algebraists S.Chakrabarti, S. Gangopahyay, S. Pal and also with Russian participants V.T. Markov, A.E. Pankratiev. The aim of projects is a study of algebraic properties of finite polynomially complete quasigroups, the problem of their recognition from its Latin square and constructions of polynomially complete quasigroups of sufficiently large order. We are also interested in poly nomially complete quasigroups with no subquasigroups. There are found sufficient conditions of polynomial completeness of a quasigroups $Q$ in terms of a group $G(Q)$. For example it suffices if $G(Q)$ acts doubly transitive in $Q$. There is found a behaviour of $G(Q)$ under isotopies. It is shown that any finite quasigroup can be embedded into a polynomial complete one. The results are applied for securing an information.
Keywords: quasigroups, Latin squres, permutation groups, transitivity. 
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     author = {V. A. Artamonov},
     title = {Quasigroups and their applications},
     journal = {\v{C}eby\v{s}evskij sbornik},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a8/}
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V. A. Artamonov. Quasigroups and their applications. Čebyševskij sbornik, Tome 19 (2018) no. 2, pp. 111-122. http://geodesic.mathdoc.fr/item/CHEB_2018_19_2_a8/