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On the Number of Conjugates of N-Ary Ouasigroups

Published online by Cambridge University Press:  20 November 2018

Mary McLeish
Mary McLeish*
Affiliation:
University of Alberta, Edmonton, Alberta
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 637 - 654
Copyright
Copyright © Canadian Mathematical Society 1979

References

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