Results 111 to 120 of about 5,491 (151)

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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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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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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Connected Orbits in Topological Generalized Quadrangles

Results in Mathematics, 1996
The authors consider the subgeometries generated by special subsets of a topological generalized quadrangle \(Q\) [as defined by the reviewer and \textit{N. Knarr} in Topology Appl. 34, No. 2, 139-152 (1990; Zbl 0692.51008)]. For example, they show that every nonempty open subset generates \(Q\), if \(Q\) is not discrete. The paper aims at applications
Stroppel, Bernhild, Stroppel, Markus
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Triangular extended generalized quadrangles

Geometriae Dedicata, 1991
In this paper, we continue the study from [2] of what are now called triangular extended generalized quadrangles. In particular, we determine all parameter sets such that the point graph is strongly regular with intersection number μ=2(t+1).
P.H. Fisher, S.A. Hobart
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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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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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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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Classical Klingenberg generalized quadrangles

Archiv der Mathematik, 1990
A Klingenberg generalized quadrangle is an incidence structure with neighbour relation having an ordinary generalized quadrangle as epimorphic image. Some infinite classes of examples are obtained using polarities in projective Klingenberg spaces.
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Generalized Quadrangles with Parallelism

1982
Publisher Summary This chapter discusses generalized quadrangles, defining generalized quadrangles (S, R) with parallelism.
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