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Quasigroups Orthogonal to a Given Abelian Group

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 this note we prove the following theorem, which does not seem to appear explicitly in the literature.

Theorem. Let A be a finite abelian group and p the smallest prime which divides |A|. Then there are p—1 mutually orthogonal quasigroups of order |A|, one of which is A.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 117
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Johnson, D. M., Dulmage, A. L. and Mendelsohn, N. S., Orthomorphisms of groups and orthogonal latin squares. I. Canad. J. Math. 13 (1961), 356-372.Google Scholar