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The previous paper was concerned with systems of equations over a certain family  of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family  of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families  that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.

Families of quasigroup operations satisfying the generalized distributive law