Hamiltonian selfdistributive quasigroups

Dolors Herbera, Tomáš Kepka, Petr Němec

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

The problem of the existence of non-medial distributive hamiltonian quasigroups is solved. Translating this problem first to commutative Moufang loops with operators, then to ternary algebras and, finally, to cocyclic modules over ℤ [x, x-1, (1-x)-1], it is shown that every non-medial distributive hamiltonian quasigroup has at least 729 elements and that there are just two isomorphism classes of such quasigroups of the least cardinality. The quasigroups representing these two classes are anti-isomorphic. © 2005 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)70-104
JournalJournal of Algebra
Volume289
DOIs
Publication statusPublished - 1 Jul 2005

Keywords

  • Distributive
  • Hamiltonian
  • Medial
  • Quasigroup

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