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- W2032735174 abstract "We shall coordinatize generalized quadrangles with a regular spread by means of a Steiner system ( P , L ) , a set X and a certain nice map Δ : P × P → Sym ( X ) . We shall then show how this coordinatization method can be used to improve a result independently obtained by Kantor [W.M. Kantor, Note on span-symmetrical generalized quadrangles, Adv. Geom. 2 (2) (2002) 197–200] and Thas [K. Thas, Classification of span-symmetric generalized quadrangles of order s , Adv. Geom. 2 (2) (2002) 189–196] stating that a generalized quadrangle of order s ≥ 2 is isomorphic to W ( s ) if it has a hyperbolic line all of whose points are centres of symmetry. We shall show that if a generalized quadrangle Q of order s ≥ 2 has a hyperbolic line containing only regular points, then all these points are also centres of symmetry. Combining this with the above-mentioned result independently obtained by Kantor and Thas, we then obtain that Q is isomorphic to the symplectic quadrangle W ( s ) ." @default.
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- W2032735174 date "2008-01-01" @default.
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- W2032735174 title "A coordinatization structure for generalized quadrangles with a regular spread" @default.
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- W2032735174 doi "https://doi.org/10.1016/j.ejc.2006.09.004" @default.
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