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IMCS/Publications/QRS/Issues/QRS v.17, n.2 (22), 2009/

Generalized quadratic quasigroup equations with tree variables

Authors: A. Krapez

Abstract

F. M. Sokhats'kyi recently posed the problem of classification of (un)cancellable generalized quadratic quasigroup equations. Refining relevant results of S. Krstic, A. Krapez and D. Zivkovic solved this problem by reducing it to the classification of connected (3-connected) cubic graphs. They also started systematic investigation by solving all equations with two variables. Here we consider equations with exactly three variables. There are 330 of them and they split into five classes of parastrophical equivalence. We give solutions to five representative equations, one from each class.




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