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Principal Loop-Isotopes of Quasigroups

Published online by Cambridge University Press:  20 November 2018

B. F. Bryant  and
Hans Schneider
B. F. Bryant
Affiliation:
Vanderbilt Universityand University of Wisconsin
Hans Schneider
Affiliation:
Vanderbilt Universityand University of Wisconsin
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If a quasigroup (L, .) has finite order n, then there are n2 principal loop-isotopes. Some of these n2 loops may be isomorphic, and the main purpose of this paper is to obtain theorems that describe the isomorphism classes. Using these results and a computer, we have determined all the loops of order 6. These are listed (using the Fisher and Yates (2) designations) at the end of the paper.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 120 - 125
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Bruck, R. H., A survey of binary systems (Berlin-Göttingen-Heidelberg, 1958).Google Scholar
2. Fisher, R. A. and Yates, F., The 6 × 6 Latin squares, Proc. Cambridge Philos. Soc, 30 (1934), 492–507.Google Scholar