Results 161 to 170 of about 12,289 (205)

Extended generalized quadrangles

Geometriae Dedicata, 1990
Extended generalized quadrangles (roughly, connected structures whose every residue is a generalized quadrangle) are studied in some detail, especially those which are uniform or strongly uniform. Much basic structure theory is developed, many examples are given, and something approaching characterization is given for many types.
CAMERON P., HUGHES D., PASINI A.
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Symmetry in Generalized Quadrangles

Designs, Codes and Cryptography, 2003
In this paper some new points of view about Lenz(-Barlotti)-type classification of finite generalized quadrangles are described. Also, it is shown that each span-symmetric generalized quadrangle of order \(s>1\) with \(s\) even is isomorphic to \(Q(4,5)\) without using the canonical connection between groups of order \(s^3-s\) with a 4-gonal basis and ...
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Finite Moufang generalized quadrangles

Journal of Mathematical Sciences, 2006
In 2002, the full classification of generalized polygons appeared [in \textit{J. Tits} and \textit{R. M. Weiss}, Moufang polygons. Springer Monographs in Mathematics. Berlin: Springer (2002; Zbl 1010.20017)]. In this paper it are reviewed some equivalent Moufang conditions for (finite) generalized quadrangles and the geometric classification in the ...
Thas, J. A., Van Maldeghem, H.
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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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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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