Symmetry in Finite Generalized Quadrangles

Koen Thas - Collection Frontiers in Mathematics

215 pages, parution le 04/02/2004

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Résumé

In this monograph finite generalized quadrangles are classified by symmetry, generalizing the celebrated Lenz-Barlotti classification for projective planes. The book is self-contained and serves as introduction to the combinatorial, geometrical and group-theoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles, including automorphism groups, elation and translation generalized quadrangles, generalized ovals and generalized ovoids, span-symmetric generalized quadrangles, flock geometry and property (G), regularity and nets, split BN-pairs of rank 1, and the Moufang property.

Written for:
Graduate and postgraduate students, researchers in geometry

Sommaire

Introduction: History, Motivation
Finite Generalized Quadrangles
Elation Generalized Quadrangles, Translation Generalized Quadrangles and Flocks
The Known Generalized Quadrangles
Substructures of Finite Nets
Symmetry Class I: Generalized Quadrangles with Axes of Symmetry
Symmetry Class II: Concurrent Axes of Symmetry in Generalized Quadrangles
Symmetry Class II: Span-Symmetric Generalized Quadrangles
Generalized Quadrangles with Distinct Translation Points
The Classification Theorem
Symmetry Class IV.3: TGQs which Arise from Flocks
A Characterization Theorem and a Classification Theorem
Symmetry Class V
Recapitulation of the Classification Theorem
Semi Quadrangles
Appendices
References

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Koen Thas
Collection	Frontiers in Mathematics
Parution	04/02/2004
Nb. de pages	215
Format	17 x 24
Couverture	Broché
Poids	472g
Intérieur	Noir et Blanc
EAN13	9783764361587