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Journal of Geometry

, Volume 21, Issue 1, pp 184–200 | Cite as

Representations of SL(2,4) on translation planes of even order

  • Norman L. Johnson
Article

Abstract

A representation for SL(2,4) In characteristic 2 is given which leads to a group theoretic construction of the Dempwolff plane of order 16. Using this construction,it is further shown that the Dempwolff plane may be obtained by the derivation of the semifield plane of order 16 and kern GF(2).

Keywords

Translation Plane Theoretic Construction Semifield Plane Group Theoretic Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    P. Dembowski.Finite Geometries. Berlin-Heidelberg-New York: Springer-Verlag.Google Scholar
  2. [2]
    U. Dempwolff. Einige Translationsebenen der Ordnung 16 und Ihre Kollineationen (to appear).Google Scholar
  3. [3]
    D.A. Foulser, N.L. Johnson, T.G. Ostrom. Characterization of the Desarguesian planes of order q2 by SL(2,q) (to appear) Internat. J. Math.Google Scholar
  4. [4]
    Ch. Hering. On shears of translation planes. Abh. Hamburg Math. Sem. 27(1972), 258–268.Google Scholar
  5. [5]
    N.L. Johnson. The translation planes of order 16 which admit nonsolvable collineation groups (to appear).Google Scholar
  6. [6]
    —. The translation planes of order 16 that admit SL(2,4). Annals Discrete Math. 14(1982), 225–236.Google Scholar
  7. [7]
    —. The translation planes of Dempwolff. Canad. J. Math. 33, no. 5 (1981), 1060–1073.Google Scholar
  8. [8]
    —. Translation planes constructed from semifield planes. Pacific J. Math. (3) 36(1971), 701–711.Google Scholar
  9. [9]
    —. A note on the derived semifield planes of order 16. Aeq. Math. 18(1978), 103–111.Google Scholar
  10. [10]
    N.L. Johnson and T.G. Ostrom. The geometry of SL(2,q) in translation planes of even order. Geom. Ded. 8(1979), 39–60.Google Scholar
  11. [11]
    E. Kleinfeld. Techniques for enumerating Veblen-Wedderburn systems. J. Assoc. Comput. Mach. 7(1960), 330–337.Google Scholar
  12. [12]
    T.G. Ostrom. Semi-translation planes. Trans. Amer. Math. Soc. 111(1964), 1–18.Google Scholar
  13. [13]
    —. Linear transformations and collineations of translation planes. J. Algebra (3) 14(1970), 405–416.Google Scholar

Copyright information

© Birkhäuser Verlag 1983

Authors and Affiliations

  • Norman L. Johnson
    • 1
  1. 1.Department of MathematicsThe University of IowaIowa City

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