Classification results in quasigroup and loop theory via a combination of automated reasoning tools

Volker Sorge, Simon Colton, Roy McCasland, Andreas Meier

Research output: Contribution to journalArticleResearchpeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)319-339
Number of pages21
JournalCommentationes Mathematicae Universitatis Carolinae
Issue number2
Publication statusPublished - 2008
Externally publishedYes


  • Automated reasoning
  • Classification
  • Loops
  • Quasigroups

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