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.
Keywords finite generalized quadrangle - (0,1)-geometry - regular abelian group
AMS Classification 05B10 - 05B25 - 05E20 - 20B25 - 51E12 - 51E20
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).