Geodesic
Principal Loop-Isotopes of Quasigroups
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 120-125

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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. 
Bryant, B. F.; Schneider, Hans. Principal Loop-Isotopes of Quasigroups. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 120-125. doi: 10.4153/CJM-1966-016-8
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[1] 1. Bruck, R. H., A survey of binary systems (Berlin-Göttingen-Heidelberg, 1958). Google Scholar

[2] 2. Fisher, R. A. and Yates, F., The 6 × 6 Latin squares, Proc. Cambridge Philos. Soc, 30 (1934), 492–507. Google Scholar

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