The Ghinelli–Löwe construction of generalized quadrangles

In 1994 Ghinelli and Löwe announced an abstract construction of finite generalized quadrangles (GQ) of order (q2,q) where q=p2n, p a prime. With a computer search they actually obtained several examples with p≡3 (mod 4) and n=1. s paper we offer a brief summary of the construction and an indication of the proof that the examples actually produced are of Kantor–Knuth type whose point-line duals are translation GQ of dimension 2 over their kernel.