Geodesic
On the structure of finite medial quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2005), pp. 11-18.

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Some variants of Toyoda, Murdoch and Ježek-Kepka theorems on medial quasigroups are given. The structure of finite medial quasigroups is described 
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V. A. Shcherbacov. On the structure of finite medial quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2005), pp. 11-18. http://geodesic.mathdoc.fr/item/BASM_2005_1_a1/

[1] Belousov V. D., Foundations of the quasigroup and loop theory, Nauka, Moscow, 1967 (in Russian) | MR

[2] Belousov V. D., Elements of quasigroup theory, A special course, Kishinev, 1981 (in Russian)

[3] Pflugfelder H. O., Quasigroups and loops: Introduction, Heldermann Verlag, Berlin, 1990 | MR

[4] Murdoch D. C., “Structure of abelian quasigroups”, Trans. Amer. Math. Soc., 47 (1941), 134–138 | MR | Zbl

[5] Toyoda K., “On axioms of linear functions”, Proc. Imp. Acad. Tokyo, 17 (1941), 221–227 | DOI | MR | Zbl

[6] Bruck R. H., “Some results in the theory of quasigroups”, Trans. Amer. Math. Soc., 55 (1944), 19–52 | DOI | MR | Zbl

[7] Jez̆ek J., Kepka T., “Varieties of abelian quasigroups”, Czech. Mathem. J., 27 (1977), 473–503 | MR | Zbl

[8] Jez̆ek J., Kepka T., “Medial groupoids”, Rozpravy C̆eskoslovenske Academie VĔD, Roçnik 93, seşit 2, Academia, Praha, 1983 | MR

[9] Shcherbacov V. A., “On structure of finite $n$-ary medial quasigroups and automorphism groups of these quasigroups”, Quasigroups and Related Systems, 13:1 (2005), 125–156 | MR

[10] Shcherbacov V. A., “On simple $n$-ary medial quasigroups”, NATO Science Series III. Computer and Systems Sciences, Proceedings of Conference “Computational Commutative and Non-Commutative Algebraic Geometry”, 196, IOS Press, 305–323 | MR

[11] Kargapolov M. I., Merzlyakov Yu. I., Foundations of the Group Theory, Nauka, Moskva, 1977 (in Russian) | MR | Zbl

[12] Kepka T., Nĕmec P., “$T$-quasigroups, II”, Acta Universitatis Carolinae, Math. et Physica, 12:2 (1971), 31–49

[13] Nĕmec P., Kepka T., “$T$-quasigroups, I”, Acta Universitatis Carolinae, Math. et Physica, 12:1 (1971), 39–49 | MR

[14] Shcherbacov V. A., “On leftdistributive quasigroups isotopic to groups”, Proceedings of the XI Conference of Young Scientists of Friendship of Nations University (Moskva, 1988), 148–149 (in Russian)

[15] Shcherbacov V. A., “On Bruck-Toyoda-Murdoch theorem and isomorphisms of some quasigroups”, First Conference of the Mathematical Society of the Republic Moldova (Chişinău, August 16–18, 2001), 138–139