A new family of extended generalized quadrangles.
Fra, Alberto Del.
Pasechnik, Dmitrii V.
Date of Issue1997
School of Physical and Mathematical Sciences
For every hyperovalOofPG(2,q) (qeven), we construct an extended generalized quadrangle with point-residues isomorphic to the generalized quadrangleT*2(O) of order(q-1, q+1).These extended generalized quadrangles are flag-transitive only whenq=2 or 4. Whenq=2 we obtain a thin-lined polar space with four planes on every line. Whenq=4 we obtain one of the geometries discovered by Yoshiara . That geometry is produced in  as a quotient of another one, which is simply connected, constructed in  by amalgamation of parabolics. In this paper we also give a ‘topological’ construction of that simply connected geometry.
European Journal of Combinatorics
© 1997 Academic Press Limited. This is the author created version of a work that has been peer reviewed and accepted for publication by European Journal of Combinatorics, Academic Press Limited. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: DOI [http://dx.doi.org/10.1006/eujc.1995.0091].