Geodesic
On isotopies, parastrophies, and orthogonality of quasigroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 237-244 
K. K. Shchukin. On isotopies, parastrophies, and orthogonality of quasigroups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 237-244. http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a15/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In V. D. Belousov's papers, some properties of parastrophes were studied and some relations between parastrophes of a given quasigroup were obtained. Also some invariants of a parastrophy were found. This article continues our paper with V. V. Gushan, in which minimal sets of parastrophe systems for quasigroups of order $6$ were obtained and some questions about orthogonality of parastrophes of a given quasigroup were studied as well.

[1] Belousov V. D., Parastrofo-ortogonalnye kvazigruppy., In-t mat. AN Moldavskoi SSR, Kishinëv, 1963 | MR

[2] Belousov V. D., “O gruppe, assotsiirovannoi kvazigruppe”, Mat. issledovaniya, 4:3 (1969), 27–39 | MR

[3] Belousov V. D., Elementy teorii kvazigrupp, Kishinëv, 1981 | Zbl

[4] Schukin K. K., Gushan V. V., “Predstavlenie parastrofov lup i kvazigrupp”, Diskret. mat., 16:4 (2004), 149–157 | DOI

[5] Shchukin K. K., “On isotopy, parastrophy and orthogonality of quasigroups”, Bul. Acad. Şti. Rep. Moldova Mat., 2010, no. 3, 29–34 | MR | Zbl