Skip to main content
Log in

Beispiele endlicher und unendlicher K-Loops

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this note examples are given for non trivial K-loops. There are commutative examples as well as non commuative, finite examples as well as infinite. Furthermore it will be shown that under an additional condition K-loops and Brück loops coincide.

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

Literatur

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

    Article  MathSciNet  Google Scholar 

  2. Burn, R. P. Finite Bol loops. Math. Proc. Cambridge Philos. Soc. 84 (1978), 377–385

    Article  MathSciNet  MATH  Google Scholar 

  3. Chein, O., Pflugfelder, H.O., Smith, J. D. H.: Quasigroups and Loops, Theory and Applications. Heldermann Verlag, Berlin 1990

    Google Scholar 

  4. Glauberman, G.: On Loops of Odd Order. J. Algebra 1 (1966), 374–396

    Article  MathSciNet  Google Scholar 

  5. Karzel, H.: Zusammenhänge zwischen Fastbereichen, scharf zweifach transitven Permutationsgruppen und 2-Strukturen mit Rechtecksaxiom. Abh. Math Sem. Univ. Hamburg 32 (1968), 191–206

    Article  MathSciNet  MATH  Google Scholar 

  6. Kist, G.: Theorie der verallgemeinerten kinematischen Räume. Beiträge zur Geometrie und Algebra 14, TUM— Bericht M 8611, München 1986

  7. Niederreiter, H. and Robinson, K. H.: Bol loops of order pq. Math. Proc. Cambridge Philos. Soc. 89 (1981), 241–256

    Article  MathSciNet  MATH  Google Scholar 

  8. Robinson, D. A.: Bo1-Loops. Trans Amer. Math. Soc. 123 (1966), 341–354

    Article  MathSciNet  Google Scholar 

  9. Ungar, A., A.: Thomas rotation and the parametrization of the Lorentz transformation group. Found. Phys. Lett. 1 (1988), 57–89

    Article  MathSciNet  Google Scholar 

  10. Ungar, A.,A.: Weakly associative groups. Res. Math. 17(1990), 149–168

    Article  MathSciNet  MATH  Google Scholar 

  11. WÄhling, H.: Theorie der Fastkörper. Thales Verlag, Essen 1987

    MATH  Google Scholar 

  12. Wefelscheid, H.: K-Loops and their use in the theory of special relativity. Preprint

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kreuzer, A. Beispiele endlicher und unendlicher K-Loops. Results. Math. 23, 357–362 (1993). https://doi.org/10.1007/BF03322307

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322307

Keywords

Navigation