Generalized quadrangles of order (s,s2). IV Translations, Moufang and Fong-Seitz

Abstract

In the period 1994-1999 the author wrote a series of three papers on generalized quadrangles of order (s,s2). In this Part IV we classify all finite translation generalized quadrangles of order (s,s2) having a kernel of size at least 3, containing a regular line not incident with the translation point. There are several applications on generalized quadrangles of order (s,s2) having at least 2 translation points, on Moufang quadrangles, and concerning the theorem of Fong and Seitz classifying all groups with a BN-pair of rank 2.