Parastrophes of quasigroups. (Q2798964)

In this paper the author studies conjugates or parastrophes of a quasigroup that can be divided into separate classes containing isotopic conjugates. He proves that the number of such classes is always 1, 2, 3 or 6. The author says that the number of such classes depends on the existence of an anti-isotopism of a quasigroup and some parastrophe of it. In section 2, the author presents a classification of parastrophes. In section 3, he presents characterizations of parastrophes of several classical types of quasigroups. He characterizes quasigroups having a fixed number of such classes. The author starts with parastrophes of IP-quasigroups. As a consequence of the results, the author gets some well-known facts presented in [\textit{V. D. Belousov}, Grundlagen der Theorie der Quasigruppen und Loops (Russian). Moskau: Verlag `Nauka' (1967; Zbl 0163.01801)]. In section 4, the author presents some consequences of the study.