Commutative Semifields of Rank 2 Over Their Middle Nucleus

  • Simeon Ball
  • Michel Lavrauw


This article is about finite commutative semifields that are of rank 2 over their middle nucleus, the largest subset of elements that is a finite field. These semifields have a direct correspondence to certain flocks of the quadratic cone in PG(3, q) and to certain ovoids of the parabolic space Q(4, q). We shall consider these links, the known examples and non-existence results.


Projective Plane Finite Field Internal Point Generalize Quadrangle Translation Plane 
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© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Simeon Ball
    • 1
  • Michel Lavrauw
    • 2
  1. 1.Queen MaryUniversity of LondonLondonUK
  2. 2.Eindhoven University of TechnologyEindhovenThe Netherlands

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