Results 211 to 220 of about 728 (237)

Groups of Projectivities of Generalized Quadrangles

Geometriae Dedicata, 1998
For some reason the study of groups of projectivities of generalized quadrangles did not yet receive the attention due, although the study of groups of projectivities of projective planes produced a number of remarkable classification results. This paper rights this wrong.
Brouns, Leen, Tent, Katrin, Van Maldeghem, Hendrik   +2 more
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Characterizations of Translation Generalized Quadrangles

Designs, Codes and Cryptography, 2001
If \(x\) is a regular point of the generalized quadrangle \({\mathcal S}\) of order \((s,t)\), \(s\neq 1\neq t\), then \(x\) defines a dual net \({\mathcal N}^*_x\). In this paper a particular class of collineations, called transvections with axis \(x\), of the point-line dual of \({\mathcal N}^*_x\), has been introduced. If \({\mathcal S}\) contains a
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Generalized Quadrangles with an Abelian Singer Group

Designs, Codes and Cryptography, 2006
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Stefaan De Winter, Koen Thas
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Affine Generalized Quadrangles – An Axiomatization

Geometriae Dedicata, 2001
A geometric hyperplane of a generalized quadrangle \({\mathcal S} = (P,{\mathcal L})\) (with pointset \(\mathcal P\) and lineset \(\mathcal L\)) is a proper subset \(H\) of \(\mathcal S\) such that for every line \(l\in\mathcal L\) either \(l\subseteq H\) or \(l\) meets \(H\) in a single point. The author shows that if \(H\) is a (geometric) hyperplane
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On Summary Equation Generated by a Quadrangle

Russian Mathematics, 2018
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Nets and generalized quadrangles

Geometriae Dedicata, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ghinelli, Dina, Ott, Udo
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A problem on generalized quadrangles

Journal of Statistical Planning and Inference, 1998
Let \({\mathcal S}=(P,B,I)\) be a generalized quadrangle of order \((s,t)\), \(s>1\), \(t>1\). Let \(p\) be a distinguished point of \(\mathcal S\) and \(G\) a group of collineations of \(\mathcal S\) acting regularly on the \(s^2t\) points of \(P-p^\bot\). In this case \(({\mathcal S}_p,G)\) is called a homogeneous generalized quadrangle (HGQ). If \(G\
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Translation generalized quadrangles

Archiv der Mathematik, 1996
A translation generalized quadrangle (TGQ) is a generalized quadrangle admitting a (uniquely determined) abelian group \(T\) of collineations fixing each line passing through some point \(\infty\) and acting transitively (and therefore regularly) on the set of points opposite to \(\infty\). Finite TGQ have been introduced by \textit{J. A. Thas} in Atti
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Generalized quadrangles with valuation

Geometriae Dedicata, 1990
We show that the class of generalized quadranges with valuation (as defined in [13]) coincides with the class of the generalized quadrangles associated with the building at infinity of affine buildings of type \(\tilde C_2\) (up to duality).
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Coordinatization of Generalized Quadrangles

1988
Publisher Summary This chapter discusses a coordinatization method for any thick generalized quadrangle (GQ) using a new algebraic structure—that is, a quadratic quaternary ring. A generalized quadrangle is an incidence structure S = (P, L, I) with point set P and line set L, satisfying the following axioms: (1) each point is incident with 1 + t ...
G. Hanssens, H. Van Maldeghem
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