On the Number of Conjugates of N-Ary Ouasigroups
- 1 June 1979
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 31 (3) , 637-654
- https://doi.org/10.4153/cjm-1979-064-6
Abstract
Higher dimensional quasigroups (a set Q with a cancellative, n-ary operation 〈 〉, ([2]) have been studied by T. Evans ([3], [4]), A. Cruse [1], C. C. Lindner ([10], [11]) and also by many others under the guise of magic cubes, Graeco-latin cubes, etc. Conjugates or parastrophes have been discussed by S. K. Stein [18], A. Sade [17] and more recently by C. C. Lindner and D. Steedley in [14], where it is shown that ordinary quasigroups exist of every order ≧ 4 with a prescribed number of distinct conjugates. It is suggested that the problem be extended to n-ary quasigroups.Keywords
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