Abstract: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.
Keywords: quasigroups, loops, classification, automated reasoning
AMS Subject Classification: 20N05