ABSTRACT
The notation xy is shorthand for (x · y). So, for example, the first quasigroup identity is actually (x · y) · (y · x) = x.
2.37 Remark The standard construction techniques for finite models of the short conjugateorthogonal identities combine the direct constructions from finite fields with recursive constructions, including the familiar direct product construction and its numerous generalizations in the form of the singular direct product construction. Pairwise balanced designs (PBDs) are of fundamental importance in the recursive construction of two-variable quasigroup models, and Theorem 2.38 is used extensively.
