Subquadrangles of order s of generalized quadrangles of order (s,s2), Part III

Abstract: In this paper, we investigate subquadrangles of order s of flock generalized quadrangles of order , s odd, with base point , where the subquadrangle does not contain the point . We prove that if the flock generalized quadrangle has such a subquadrangle, then is classical. This solves “Remaining case (a)” in Brown and Thas [M.R. Brown, J.A. Thas, Subquadrangles of order s of generalized quadrangles of order , II, J. Combin. Theory Ser. A 106 (2004) 33–48] (“Remaining case (b)” was already handled in K. Thas [K. Thas, Symmetrieën in eindige veralgemeende vierhoeken (Symmetries in finite generalized quadrangles), Master thesis, Ghent University, Ghent, 1999, 186 p.]). As a corollary we have: if is an egg in for which the translation dual is good at the tangent space of at its element π and if there is a pseudo-oval on not containing π, then is classical. As a byproduct we prove that if the flock GQ of order , s odd, has a regular point x collinear with, but distinct from, the base point , then is a translation generalized quadrangle with base line . [Copyright &y& Elsevier]