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Generalized Quadrangles with an Abelian Singer Group

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Abstract

In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.

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References

  1. T. Beth D. Jungnickel H. Lenz (1999) Design Theory Encyclopedia of Mathematics and its Applications. Cambridge University Press Cambridge

    Google Scholar 

  2. F. De Clerck, H. Gevaert and J. A. Thas, Translation partial geometries, Combinatorics ’86 (Trento 1986), Ann. Discrete Math., Vol. 37, North Holland (1988) pp. 117–135.

  3. B. N. Cooperstein J. A. Thas (2001) ArticleTitleOn generalized k-arcs in \(\mathbb{PG}(2n,q)\) Ann. Comb. 5 141–152 Occurrence Handle2003c:51005

    MathSciNet  Google Scholar 

  4. S. Winter ParticleDe (2004) ArticleTitleElation and translation semipartial geometries J. Combin. Theorey Ser. 108 313–330 Occurrence Handle1076.51005

    MATH  Google Scholar 

  5. D. Ghinelli (1992) ArticleTitleRegular groups on generalized quadrangles and nonabelian difference sets with multiplier −1 Geom. Dedicata 41 165–174 Occurrence Handle10.1007/BF00182417 Occurrence Handle0746.51011 Occurrence Handle93c:51006

    Article  MATH  MathSciNet  Google Scholar 

  6. D. R. Hughes F. C. Piper (1973) Projective Planes Springer-Verlag New York/Heidelberg/Berlin

    Google Scholar 

  7. S. E. Payne J. A. Thas (1984) Finite Generalized Quadrangles Pitman Advanced Publishing Program Boston/London/Melbourne

    Google Scholar 

  8. J. A. Thas and K. Thas, Translation generalized quadrangles in even characteristic, Combinatorica, to appear.

  9. H. Maldeghem ParticleVan (1998) Generalized Polygons Birkhäuser Verlag Basel

    Google Scholar 

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Correspondence to S. De Winter.

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Communicated by:M. de Resmini

S. De Winter: The first author is a Research Assistant of the Fund for Scientific Research—Flanders (Belgium).

K. Thas: The second author is a Postdoctoral Fellow of the Fund for Scientific Research—Flanders (Belgium).

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De Winter, S., Thas, K. Generalized Quadrangles with an Abelian Singer Group. Des Codes Crypt 39, 81–87 (2006). https://doi.org/10.1007/s10623-005-2747-z

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  • DOI: https://doi.org/10.1007/s10623-005-2747-z

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