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.
Similar content being viewed by others
References
T. Beth D. Jungnickel H. Lenz (1999) Design Theory Encyclopedia of Mathematics and its Applications. Cambridge University Press Cambridge
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.
B. N. Cooperstein J. A. Thas (2001) ArticleTitleOn generalized k-arcs in \(\mathbb{PG}(2n,q)\) Ann. Comb. 5 141–152 Occurrence Handle2003c:51005
S. Winter ParticleDe (2004) ArticleTitleElation and translation semipartial geometries J. Combin. Theorey Ser. 108 313–330 Occurrence Handle1076.51005
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
D. R. Hughes F. C. Piper (1973) Projective Planes Springer-Verlag New York/Heidelberg/Berlin
S. E. Payne J. A. Thas (1984) Finite Generalized Quadrangles Pitman Advanced Publishing Program Boston/London/Melbourne
J. A. Thas and K. Thas, Translation generalized quadrangles in even characteristic, Combinatorica, to appear.
H. Maldeghem ParticleVan (1998) Generalized Polygons Birkhäuser Verlag Basel
Author information
Authors and Affiliations
Corresponding author
Additional information
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).
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10623-005-2747-z