Symmetry in Finite Generalized Quadrangles
(Sprache: Englisch)
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...
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Klappentext zu „Symmetry in Finite Generalized Quadrangles “
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.
Inhaltsverzeichnis zu „Symmetry in Finite Generalized Quadrangles “
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.
Bibliographische Angaben
- Autor: Koen Thas
- 2004, 2004, 214 Seiten, Maße: 17,8 x 25,4 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3764361581
- ISBN-13: 9783764361587
- Erscheinungsdatum: 26.01.2004
Sprache:
Englisch
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