Subquadrangles of order <f>s</f> of generalized quadrangles of order <f>(s,s2)</f>, Part I

In this paper, subquadrangles of order <f>s</f> of generalized quadrangles (GQs) of order <f>(s,s2)</f> are investigated. In the case where <f>S</f> is a dual flock GQ of order <f>(s,s2)</f>, <f>s</f> even, the classification of subquadrangles of order <f>s</f> is completed. In the case where <f>E</f> is an egg good at an element and the corresponding translation generalized quadrangle <f>T(E)</f> of order <f>(s,s2)</f>, <f>s</f> even, has base point <f>(∞)</f> it is proved that if <f>T(E)</f> has a subquadrangle of order <f>s</f> not containing <f>(∞)</f>, then <f>T(E)</f> is the classical GQ <f>Q(5,s)</f>. Also a new strong characterization of the classical GQ <f>Q(5,s)</f>, <f>s</f> even or odd, is obtained. In Part II, the case <f>s</f> odd is considered. [Copyright &y& Elsevier]