The Ghinelli-Löwe construction of generalized quadrangles

In 1994 Ghinelli and Lowe 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.In this 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.