Symmetry in Finite Generalized Quadrangles
Springer Basel (Verlag)
978-3-7643-6158-7 (ISBN)
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.
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.
| Erscheint lt. Verlag | 26.1.2004 |
|---|---|
| Reihe/Serie | Frontiers in Mathematics |
| Zusatzinfo | XXI, 214 p. |
| Verlagsort | Basel |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 475 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | automorphism • Boundary element method • Character • classification • Finite • Geometrie • Geometry • Hardcover, Softcover / Mathematik/Geometrie • HC/Mathematik/Geometrie • History of Mathematics • Lenz-Barlotti-Klassifikation • Morphism • Story • symmetry • Theorem • Viereck |
| ISBN-10 | 3-7643-6158-1 / 3764361581 |
| ISBN-13 | 978-3-7643-6158-7 / 9783764361587 |
| Zustand | Neuware |
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