[Cherubino] Quaderni Elettronici del Seminario di Geometria Combinatoria 5E (Maggio 2002), 1--20
Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica

Dina GHINELLI and Stanley E. PAYNE
The Ghinelli-Löwe Construction of Generalized Quadrangles: An Exposition
(May 2002)

Abstract. In 1994 D. Ghinelli and S. Löwe circulated the preprint "Fourgonal Families from Nonsymmetric Matrices" giving a recipe for constructing finite generalized quadrangles of order (q2,q) where q=p2n, p a prime. A computer search located several examples with p congruent to 3 modulo 4 and n = 1, where all the ingredients were present so that a GQ was actually obtained, but it was never determined whether or not the GQ were isomorphic to some previously known examples. Recently the authors of the present article were able to show that the GQ are isomorphic to flock GQ arising from a semifield flock of Kantor-Knuth type where the kernel of the point-line dual translation GQ has order pn. A forthcoming article, which merely surveys the main results, is missing many details. The present exposition (which includes a major revision of the original preprint) offers many of these details to the interested reader.

AMS Subject Classification: 51E12

Authors:
Dina Ghinelli
Dipartimento di Matematica - Università di Roma "La Sapienza"
Piazzale Aldo Moro, 2 - I00185 Roma (Italy)
e-mail: dina@mat.uniroma1.it
Stanley E. Payne
Department of Mathematics - University of Colorado at Denver
Campus Box 170 - 1250 14th Street, Suite 600 (80202)
P.O. Box 173364
Denver, Colorado 80217-3364
e-mail: spayne@math.cudenver.edu
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