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The Generalized Singular Direct Product for Quasigroups

Published online by Cambridge University Press:  20 November 2018

Charles C. Lindner
Charles C. Lindner*
Affiliation:
Auburn University, Auburn, Alabama
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 61 - 63
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Mendelsohn, N. S., Latin squares orthogonal to their transposes, J. Combinatorial Theory, (to appear).Google Scholar
2. Sade, A., Produit direct-singulier de quasigroupes orthogonaux et anti-abéliens, Ann. Soc Sci. Bruxelles Sér. L, 74 (1960), 91-99.Google Scholar