Skip to main content
SpringerLink
Log in

An Affine Characterization of Moufang Projective Klingenberg Planes

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

It is shown that with minor exceptions all projective Klingenberg planes are Moufang exactly if they have a trilateral each of whose sides is the line at infinity of a translation plane; but there are non-Moufang projective Klingenberg planes which have a single line which produces an equiaffine translation plane or a point P so that all lines through P, except perhaps for some neighbour lines, produce translation planes.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. Artmann, Über die Einbettung uniformer affiner Hjelmslev-Ebenen in projektive Hjelmslev-Ebenen, Abh. Math. Sem. Univ. Hamburg 34 (1970), 127–134.

    Article  MathSciNet  MATH  Google Scholar 

  2. P. Bacon, An Introduction to Klingenberg planes, Vols. 1–4, P.Y. Bacon, Publisher, 3101 N.W. 2nd Ave. Gainsville, Fl. 32607, U.S.A. (Vol. 1, 1976; Vol. 2, 1977; Vol. 3, 1979; Vol. 4, 1983).

  3. P. Bacon, Desarguesian Klingenberg planes, Trans. Amer. Math. Soc. 241 (1978), 343–355.

    Article  MathSciNet  MATH  Google Scholar 

  4. P. Bacon, On the extension of projectively uniform affine Hjelmslev planes, Abh. Math. Sem. Univ. Hamburg 41 (1974), 185–189.

    Article  MathSciNet  MATH  Google Scholar 

  5. C. A. Baker, N.D. Lane and J. W. Lorimer, A coordinatization for Moufang projective Klingenberg planes. Preprint (1989).

  6. -, Local alternative rings and finite alternative right chain rings. Preprint (1989).

  7. M. D’Angelo, On equiaffine planes, J. Geometry 15 (1981), 74–85.

    Article  MathSciNet  MATH  Google Scholar 

  8. P. Dembowski, Finite Geometries, Springer-Verlag, New York (1968).

    Book  MATH  Google Scholar 

  9. M. Dugas, Moufang Hjelmslev-Ebenen Arch. Math. 28(1977), 318–322.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. Hughes and F. Piper, Projective Planes, Springer-Verlag, New York (1973).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Mount Allison University, Sackville, New Brunswick, Canada, EOA 3CO

    C. A. Baker

  2. Department of Mathematics and Statistics, Mcmaster University, Hamilton, Ontario, Canada, L8S 4K1

    N. D. Lane

  3. Department of Mathematics, University Of Toronto, Toronto, Ontario, Canada, M5S 1A1

    J. W. Lorimer

Authors
  1. C. A. Baker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. D. Lane
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. W. Lorimer
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baker, C.A., Lane, N.D. & Lorimer, J.W. An Affine Characterization of Moufang Projective Klingenberg Planes. Results. Math. 17, 27–36 (1990). https://doi.org/10.1007/BF03322627

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03322627

Keywords

Search

Navigation