Abstract
In V. D. Belousov’s papers, some properties of parastrophies were studied and some relations between parastrophies 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 parastrophy systems for quasigroups of order 6 were obtained and some questions about orthogonality of parastrophies of a given quasigroup were studied as well.
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References
V. D. Belousov, Parastrophy-Orthogonality Quasigroup [in Russian], Inst. Mat. AN Mold. SSR, Kishinev (1963).
V. D. Belousov, “On a group associated with a quasigroup,” Mat. Issled., 4, No. 3, 27–39 (1969).
V. D. Belousov, Elements of Quasigroup Theory [in Russian], Kishinev (1981).
K. K. Shchukin, “On isotopy, parastrophy and orthogonality of quasigroups,” Bul. Acad. Şti. Rep. Moldova, Mat., No. 3, 29–34 (2010).
K. K. Shchukin and V. V. Gushan, “Representation of parastrophies of loops and quasigroups,” Diskret. Mat., 16, No. 4, 149–157 (2004).
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Deceased.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 5, pp. 237–244, 2011/12.
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Shchukin, K.K. On isotopies, parastrophies, and orthogonality of quasigroups. J Math Sci 193, 639–644 (2013). https://doi.org/10.1007/s10958-013-1491-6
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DOI: https://doi.org/10.1007/s10958-013-1491-6