Symmetry in Finite Generalized Quadrangles

Thas, Koen

ISBN 10: 3764361581 / ISBN 13: 9783764361587

Editore: Birkhäuser, 2004

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Dati bibliografici

• Titolo: Symmetry in Finite Generalized Quadrangles
• Editore: Birkhäuser
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 3764361581
• ISBN 13: 9783764361587
• Rilegatura: Brossura
• Condizione: As New

Descrizione articolo

Riassunto

This monograph classifies finite generalized quadrangles by symmetry, generalizing the celebrated Lenz-Barlotti classification for projective planes. The book introduces 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.

Contenuti

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.