Geodesic
The Generalized Singular Direct Product for Quasigroups
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 61-63

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In [2], A. Sade gives a construction for quasigroups which he calls the singular direct product. In this paper we generalize Sades' construction. As an application we obtain a recursive construction for quasigroups orthogonal to their transposes. All quasigroups considered in this paper will be finite. 
Lindner, Charles C. The Generalized Singular Direct Product for Quasigroups. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 61-63. doi: 10.4153/CMB-1971-011-0
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[1] 1. Mendelsohn, N. S., Latin squares orthogonal to their transposes, J. Combinatorial Theory, (to appear). Google Scholar

[2] 2. Sade, A., Produit direct-singulier de quasigroupes orthogonaux et anti-abéliens, Ann. Soc Sci. Bruxelles Sér. L, 74 (1960), 91-99. Google Scholar

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