Koen Thas

Symmetry in Finite Generalized Quadrangles

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Frontiers in Mathematics
• Verlag: Birkhäuser / Birkhäuser Basel / Springer, Basel
• Artikelnr. des Verlages: 978-3-7643-6158-7
• 2004
• Seitenzahl: 240
• Erscheinungstermin: 26. Januar 2004
• Englisch
• Abmessung: 254mm x 178mm x 14mm
• Gewicht: 476g
• ISBN-13: 9783764361587
• ISBN-10: 3764361581
• Artikelnr.: 12355472

Autorenporträt

Koen Thas, University of Ghent, Belgium

Inhaltsangabe

Introduction: History, Motivation.- 1. Finite Generalized Quadrangles.- 2. Elation Generalized Quadrangles, Translation Generalized Quadrangles and Flocks.- 3. The Known Generalized Quadrangles.- 4. Substructures of Finite Nets.- 5. Symmetry Class I: Generalized Quadrangles with Axes of Symmetry.- 6. Symmetry Class II: Concurrent Axes of Symmetry in Generalized Quadrangles.- 7. Symmetry Class II: Span-Symmetric Generalized Quadrangles.- 8. Generalized Quadrangles with Distinct Translation Points.- 9. The Classification Theorem.- 10. Symmetry Class IV.3: TGQs which Arise from Flocks .- 11. A Characterization Theorem and a Classification Theorem.- 12. Symmetry Class V.- 13. Recapitulation of the Classification Theorem.- 14. Semi Quadrangles.- Appendices.- References.