Geodesic
On isotopy, parastrophy and orthogonality of quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2010), pp. 29-34.

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This paper contains new results on conditions of an isotopy of two quasigroups and their orthogonality to parastrophes. The structure of parastrophe group of a quasigroup is defined. The results of this paper complement investigations of V. D. Belousov in [1, 2] and continue studies from [3]. 
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K. K. Shchukin. On isotopy, parastrophy and orthogonality of quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2010), pp. 29-34. http://geodesic.mathdoc.fr/item/BASM_2010_3_a3/

[1] Belousov V. D., “On an associated group of a quasigroup”, Matematiceskie issledovania, Academia Nauk Moldavskoi SSR, 4:3 (1969), 27–39 (Russian) | MR

[2] Belousov V. D., “Parastrophic-orthogonal quasigroups”, Quasigroups and Related Systems, 13:1 (2005), 25–72 | MR | Zbl

[3] Shchukin K. K., Gushan V. V., “Representation of parastrophes of loops and quasigroups”, Discrete Mathematics, 16:4 (2004), 149–157 (Russian) | MR | Zbl

[4] Belousov V. D., Elements of the theory of quasigroups, A special course for students, Kishinev, 1983 (Russian)