Skip to main content
Log in

Selfdistributive groupoids of small orders

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

After enumerating isomorphism types of at most five-element left distributive groupoids, we prove that a distributive groupoid with less than 81 elements is necessarily medial.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. El. Bashir and A. Drápal: Quasitrivial left distributive groupoids. Commentationes Math. Univ. Carolinae 35 (1994), 597–606.

    Google Scholar 

  2. G. Bol: Gewebe und Gruppen. Math. Ann. 114 (1937), 414–431.

    Google Scholar 

  3. A. Drápal, T. Kepka and M. Musílek: Group conjugation has non-trivial LD-identities. Commentationes Math. Univ. Carolinae 35 (1994), 219–222.

    Google Scholar 

  4. M. Hall, Jr.: Automorphisms of Steiner triple systems. IBM J. of Research Development 4 (1960), 460–471.

    Google Scholar 

  5. J. Ježek and T. Kepka: Atoms in the lattice of varieties of distributive groupoids. Colloquia Math. Soc. J. Bolyai 14. Lattice Theory. Szeged, 1974, pp. 185–194.

    Google Scholar 

  6. J. Ježek, T. Kepka and P. Němec: Distributive groupoids. Rozpravy ČSAV, Řada mat. a přír. věd 91, Academia, Praha, 1981.

    Google Scholar 

  7. T. Kepka: Distributive division groupoids. Math. Nachr. 87 (1979), 103–107.

    Google Scholar 

  8. T. Kepka: Notes on quasimodules. Commentationes Math. Univ. Carolinae 20 (1979), 229–247.

    Google Scholar 

  9. T. Kepka and P. Němec: Commutative Moufang loops and distributive groupoids of small orders. Czech. Math. J. 31 (1981), 633–669.

    Google Scholar 

  10. J. P. Soublin: Étude algébrique de la notion de moyenne. J. Math. Pures et Appl. 50 (1971), 53–264.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ježek, J., Kepka, T. Selfdistributive groupoids of small orders. Czechoslovak Mathematical Journal 47, 463–468 (1997). https://doi.org/10.1023/A:1022459317190

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022459317190

Navigation