Geodesic
MOUFANG QUADRANGLES OF MIXED TYPE
Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 143-161

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we present some geometric characterizations of the Moufang quadrangles of mixed type, i.e., the Moufang quadrangles all the points and lines of which are regular. Roughly, we classify generalized quadrangles with enough (to be made precise) regular points and lines with the property that the dual nets associated to the regular points satisfy the Axiom of Veblen-Young, or a very weak version of the Axiom of Desargues. As an application we obtain a geometric characterization and axiomatization of the generalized inversive planes arising from the Suzuki-Tits ovoids related to a polarity in a mixed quadrangle. In the perfect case this gives rise to a characterization with one axiom less than in a previous result by the second author.
DOI : 10.1017/S0017089507004016
Mots-clés : 51E12 
STRUYVE, KOEN; MALDEGHEM, HENDRIK VAN. MOUFANG QUADRANGLES OF MIXED TYPE. Glasgow mathematical journal, Tome 50 (2008) no. 1, pp. 143-161. doi: 10.1017/S0017089507004016
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[1] 1.Buekenhout, F., Handbook of incidence geometry, buildings and foundations (North-Holland, Elsevier, 1995). Google Scholar

[2] 2.Johnson, N., The classification of subplane covered nets, Bull. Belg. Math. Soc. Simon Stevin 2 (1995), 487–508. Google Scholar

[3] 3.Payne, S. E. and Thas, J. A., Finite generalized quadrangles (Pitman, 1984). Google Scholar

[4] 4.Schroth, A. E., Characterizing symplectic quadrangles by their derivations, Arch. Math. 58 (1992), 98–104. Google Scholar

[5] 5.Tent, K., Half Moufang implies Moufang for generalized quadrangles, J. Reine Angew. Math. 566 (2004), 231–236. Google Scholar

[6] 6.Thas, J. A. and Maldeghem, H. Van, Generalized quadrangles and the axiom of Veblen, Geometry, combinatorial designs and related structures (ed. Hirschfeld, J. W. P.), London Math. Soc. Lecture Note Ser. No. 245 (Cambridge University Press, 1997), 241–253. Google Scholar

[7] 7.Tits, J., Ovoï des et groupes de Suzuki, Arch. Math. 13 (1962), 187–198. Google Scholar | DOI

[8] 8.Tits, J., Buildings of spherical type and finite BN-pairs, Lecture Notes in Math. No. 386 (Springer-Verlag, 1974). Google Scholar

[9] 9.Tits, J. and Weiss, R., Moufang polygons, (Springer-Verlag, 2002). Google Scholar

[10] 10.Van Maldeghem, H., A geometric characterization of the perfect Suzuki-Tits ovoids, J. Geom. 58 (1997), 192–202. Google Scholar

[11] 11.Van Maldeghem, H., Generalized polygons, Monographs in Math. No. 93 (Birkhauser-Verlag, 1998). Google Scholar | DOI

[12] 12.Van Maldeghem, H., On a question of Arjeh Cohen: a characterization of Moufang projective planes, Bull. Inst. Combin. Appl. 35 (2002), 11–13. Google Scholar

[13] 13.Van Maldeghem, H., Moufang lines defined by (generalized) Suzuki groups, Discrete Math., Proceedings of GAC3 (ed. W. Haemers et al.) to appear. Google Scholar

[14] 14.Veblen, O. and Young, J. W., Projective geometry (Blaisdell, 1910). Google Scholar

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