Skip to main content
SpringerLink
Log in

Towards a characterization of generalized twisted field planes

  • Published:
Journal of Geometry Aims and scope Submit manuscript

Abstract

In this work we study semifield planes of orderq n(q=p r,p prime) with a collineation whose order is ap-primitive divisor ofq n−1.

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. ALBERT, A.A., Generalized Twisted Fields.Pacif. J. Math. 11 (1961), 1–8.

    Google Scholar 

  2. CORDERO, M., Semifield Planes of Orderp 4 that Admit ap-primitive Baer Collineation.Osaka J. Math, 28 (1991), 305–321.

    Google Scholar 

  3. CORDERO, M., The Autotopism Group ofp-primitive Semifield Planes.ARS Combinatoria, 32 (1991) 57–64.

    Google Scholar 

  4. CORDERO, M., The Nuclei and Other Properties ofp-primitive Semifield Planes.Intern. J. Math. & Math. Sci., VOL. 15 No. 2 (1992) 367–370.

    Google Scholar 

  5. DEMBOWSKI, P.,Finite Geometries. Springer, New York, N.Y., 1968.

    Google Scholar 

  6. DEMPWOLFF, U., A characterization of the generalized twisted field planes.Arch. Math. 50 (1988), 477–480.

    Google Scholar 

  7. GANLEY, M. and JHA, V., On translation planes with a 2-transitive orbit on the line at infinity.Arch. Math. 47 (1986), 379–384.

    Google Scholar 

  8. HUPPERT, B.,Endliche Gruppen I. Springer-Verlag, Berlin, Heidelberg, New York, 1967.

    Google Scholar 

  9. KALLAHER, M., A survey of weak rank 3 affine planes.Proc. International Conf. Projective Planes. (Wash. State Univ., 1973), 121–143.

  10. MENICHETTI, G., On a Kaplansky Conjecture Concerning Three-Dimensional Division Algebras over a Finite Field.J. of Algebra 47 (1977), 400–410.

    Google Scholar 

  11. OYAMA, T., On quasifields.Osaka J. Math. 22, 35–54 (1985).

    Google Scholar 

  12. VAUGHN, T. P., Polynomials and linear transformations over finite fields. J. Reine Angew. Math. 262 (1974), 199–206.

    Google Scholar 

  13. ZSIGMONDY K., Zur Theorie der Potenzreste.Monatsh für Math. u. Phys. 3 (1892), 265–284.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Texas Tech University, 79409, Lubbock, Texas

    Minerva Cordero

  2. Department of Mathematics, University of Puerto Rico, 00931, Rio Piedras, Puerto Rico

    Raúl Figueroa

Authors
  1. Minerva Cordero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raúl Figueroa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by NSF Grant No. DMS-9107372

Research supported in part by NSF grants RII-9014056, component IV of the EPSCoR of Puerto Rico grant and ARO grant for Cornell MSI.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cordero, M., Figueroa, R. Towards a characterization of generalized twisted field planes. J Geom 52, 54–63 (1995). https://doi.org/10.1007/BF01406826

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01406826

Keywords

Search

Navigation