Classification of extended generalized quadrangles with maximum diameter (Q1199469)

A connected geometry \(S\) all of whose point residues are generalized quadrangles of order \((s,t)\) is called an extended generalized quadrangle (EGQ) of order \((s,t)\). By a result of \textit{P. J. Cameron}, \textit{D. R. Hughes} and \textit{A. Pasini} [ Geom. Dedicata 35, No. 1-3, 193-228 (1990; Zbl 0702.51005)] the diameter \(\Delta\) of \(S\) satisfies \(\Delta=s+1\). The paper under review classifies those EGQs that have the (maximum) diameter \(s+1\). The result is that \(S\) has diameter \(s+1\) if and only if \(S\) belongs to three special types: \(S\) is a certain Johnson geometry or a special affine polar space of order 2 or complete tripartite on \(3(t+1)\) points \((t>1)\).