Journal article

Generalized quadrangles with a thick hyperbolic line weakly embedded in projective space


Authors list: Steinbach, A

Publication year: 1998

Pages: 447-459

Journal: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN

Volume number: 5

Issue number: 2-3

ISSN: 1370-1444

Open access status: Hybrid

DOI Link: https://doi.org/10.36045/bbms/1103409024

Publisher: BELGIAN MATHEMATICAL SOC TRIOM


Abstract: 
Let Gamma be a generalized quadrangle weakly embedded in projective space such that {a, b}(Gamma Gamma) contains a point different from a and b, where a and b are opposite points of Gamma. We prove that Gamma admits non-trivial central elations. Further, each central elation of Gamma is induced by a special linear transformation of the underlying vector space. This generalizes a result of Lefevre-Percsy [3, Th. 1]. Furthermore, we show that Gamma is a Moufang quadrangle.



Citation Styles

Harvard Citation style: Steinbach, A. (1998) Generalized quadrangles with a thick hyperbolic line weakly embedded in projective space, BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 5(2-3), pp. 447-459. https://doi.org/10.36045/bbms/1103409024

APA Citation style: Steinbach, A. (1998). Generalized quadrangles with a thick hyperbolic line weakly embedded in projective space. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN. 5(2-3), 447-459. https://doi.org/10.36045/bbms/1103409024



Keywords

central elation; generalized quadrangle; Moufang Condition; Polar space; POLAR SPACES; transvection; weak embedding


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