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Principal Loop-Isotopes of Quasigroups

  • B. F. Bryant (a1) and Hans Schneider (a1)

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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.

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References

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1. Bruck, R. H., A survey of binary systems (Berlin-Göttingen-Heidelberg, 1958).
2. Fisher, R. A. and Yates, F., The 6 × 6 Latin squares, Proc. Cambridge Philos. Soc, 30 (1934), 492507.
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