Osaka Journal of Mathematics

A note on semifield planes admitting irreducible Planar Baer collineations

Ulrich Dempwolff

Full-text: Open access

Abstract

In this note we study finite semifield planes which admit an irreducible planar Baer collineation. This continues previous work of N. Johnson [5].

Article information

Source
Osaka J. Math., Volume 45, Number 4 (2008), 895-908.

Dates
First available in Project Euclid: 26 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1227708824

Mathematical Reviews number (MathSciNet)
MR2493961

Zentralblatt MATH identifier
1165.51001

Subjects
Primary: 51E15: Affine and projective planes
Secondary: 17A35: Division algebras

Citation

Dempwolff, Ulrich. A note on semifield planes admitting irreducible Planar Baer collineations. Osaka J. Math. 45 (2008), no. 4, 895--908. https://projecteuclid.org/euclid.ojm/1227708824


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References

  • S. Ball and M.R. Brown: The six semifield planes associated with a semifield flock, Adv. Math. 189 (2004), 68--87.
  • U. Dempwolff: Semifield planes of order 81, to appear in J. Geom.
  • Y. Hiramine, M. Matsumoto and T. Oyama: On some extension of 1-spread sets, Osaka J. Math. 24 (1987), 123--137.
  • B. Huppert: Endliche Gruppen I, Springer, Berlin, 1967.
  • N.L. Johnson: Semifield planes of characteristic $p$ admitting $p$-primitive Baer collineations, Osaka J. Math. 26 (1989), 281--285.
  • N.L. Johnson: Sequences of derivable translation planes, Osaka J. Math. 25 (1988), 519--530.
  • N.L. Johnson: private communication.
  • D.E. Knuth: Finite semifields and projective planes, J. Algebra 2 (1965), 182--217.
  • H. Lüneburg: Translation Planes, Springer, Berlin, 1980.
  • T. Oyama: On quasifields, Osaka J. Math. 22 (1985), 35--54.