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IMI/Publicaţii/BASM/Ediţii/BASM n.2(87), 2018/

Solution and full classification of generalized binary functional equations of the type (3;3;0)

Authors: Halyna Krainichuk, Fedir Sokhatsky

Abstract

Generalized binary functional quasigroup equations in two individual variables with three appearances are under consideration. There exist five classes of the equations (two equations belong to the same class if there exists a relation between sets of their solutions). The quasigroup solution sets of equations from every class are given. In addition, it is proved that every parastrophe of a quasigroup has an orthogonal mate if the quasigroup has an orthogonal mate.

Vasyl Stus Donetsk National University
Department of mathematical analysis
and differential equations
21000 Vinnytsia, Ukraine
E-mail: ,

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