Classification of generalized ternary quadratic quasigroup functional equations of the length three

F. M. Sokhatsky, A. V. Tarasevych


A functional equation is called: generalized if all functional variables are pairwise different; ternary if all its functional variables are ternary; quadratic if each individual variable has exactly two appearances; quasigroup if its solutions are studied only on invertible functions. A length of a functional equation is the number of all its functional variables.  A complete classification up to parastrophically primary equivalence of generalized quadratic quasigroup functional equations of the length three is given. Solution sets of a full family of representatives of the equivalence are found.


ternary quasigroup, quadratic equation, length of a functional equation, parastrophically primary equivalence

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