Geodesic
Realizations of Loops and Groups defined by short identities
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 373-383.

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In a recent paper, those quasigroup identities involving at most three variables and of “length” six which force the quasigroup to be a loop or group have been enumerated by computer. We separate these identities into subsets according to what classes of loops they define and also provide humanly-comprehensible proofs for most of the computer-generated results.
Classification : 20N05
Keywords: quasigroup identity; loop; group 
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     title = {Realizations of {Loops} and {Groups} defined by short identities},
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Keedwell, A. D. Realizations of Loops and Groups defined by short identities. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 373-383. http://geodesic.mathdoc.fr/item/CMUC_2009__50_3_a4/