Geodesic
Classification results in quasigroup and loop theory via a combination of automated reasoning tools
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 319-339

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We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques --- including machine learning and computer algebra --- which we present here. Moreover, each result has been automatically verified, again using a variety of techniques --- including automated theorem proving, computer algebra and satisfiability solving --- and we describe our bootstrapping approach to the generation and verification of these classification results.
Classification : 20N05, 68T15, 68W30, 81T05
Keywords: quasigroups; loops; classification; automated reasoning 
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     title = {Classification results in quasigroup and loop theory via a combination of automated reasoning tools},
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Sorge, Volker; Colton, Simon; McCasland, Roy; Meier, Andreas. Classification results in quasigroup and loop theory via a combination of automated reasoning tools. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 319-339. http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a13/