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

Abstract

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.