Subquadrangles of order s of generalized quadrangles of order (s,s(2)), Part II

摘要

In this paper, subquadrangles of order s of generalized quadrangles (GQ) of order (s, s(2)), with s odd, are investigated. The even case was considered in Part I. In the case where 0 is an egg good at an element pi and the translation generalized quadrangle Y = T(O) has order (s,s(2)), with s odd, we prove that if Y' is a subquadrangle of order s of Y, then Y' is the classical GQ Q(4, s) and either Y is the classical GQ Q(5, s) or Y' is one of the s(3) + s(2) subquadrangles of order s containing the line pi of Y. Further, some characterizations of particular eggs are obtained. Finally, it is shown that if Y is a flock GQ of order (s(2),s), s odd, with base point (infinity) and Y' is a subquadrangle of order s of Y containing the point (infinity), then Y is a Kantor semifield flock GQ Y' is isomorphic to the classical GQ W(s) and either Y is isomorphic to the classical GQ H(3, s(2)) or Y' is one of the s(3) + s(2) subquadrangles of order s containing the point (infinity). As an application there is a characterization of the Kantor semifield flock GQ in terms of the net defined by the regular point (infinity) of the flock GQ. (C) 2004 Elsevier Inc. All rights reserved.