September 2012, Volume 64, Issue 3, pp 255-263,
Open Access This content is freely available online to anyone, anywhere at any time.
A geometric proof of a theorem on antiregularity of generalized quadrangles
A geometric proof is given in terms of Laguerre geometry of the theorem of Bagchi, Brouwer and Wilbrink, which states that if a generalized quadrangle of order s > 1 has an antiregular point then all of its points are antiregular.
Communicated by J. D. Key.
This work was partially supported by a grant from the Research Grants Council of the HKSAR, China (Project number: HKU7060/11P).
- Bagchi B., Brouwer A.E., Wilbrink H.A.: Notes on binary codes related to the O(5, q) generalized quadrangle for odd q. Geom. Dedicata 39, 339–355 (1991) CrossRef
- Benson C.T.: On the structure of generalized quadrangles. J. Algebra 15, 443–454 (1970) CrossRef
- De Soete M., Thas J.A.: A characterization of the generalized quadrangle Q(4, q), q odd. J. Geom. 28, 57–79 (1987) CrossRef
- Hirschfeld J.W.P., Thas J.A.: General Galois Geometries, Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford (1991).
- Hughes D.R., Piper F.C.: Projective Planes. GTM 6. Springer, Berlin (1973)
- Mazzocca F.: Sistemi grafici rigati di seconda specie. 1st Mat. Univ. Napoli Rel. 28 (1973).
- Payne S.E., Thas J.A.: Generalized quadrangles with symmetry, Part II. Simon Stevin 49, 81–103 (1976)
- Payne S.E., Thas J.A.: Finite Generalized Quadrangles, 2nd edn. European Mathematical Society (2009).
- Thas J.A.: Circle Geometries and Generalized Quadrangles, pp. 327–352. Finite Geometries. Dekker, New York (1985)
- Thas J.A., Thas K., Van Maldeghem H.: Translation Generalized Quadrangles. Ser. Pure Math. 26, World Scientific Publishing Co. Pte. Ltd., London WC2H 9HE (2006).
- A geometric proof of a theorem on antiregularity of generalized quadrangles
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