Symmetry in Finite Generalized Quadrangles
Published on 26. January 2004
Book
Paperback/Softback
XXI, 214 pages
978-3-7643-6158-7 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XXI, 214 p.
Dimensions
Height: 254 mm
Width: 178 mm
Thickness: 14 mm
Weight
460 gr
ISBN-13
978-3-7643-6158-7 (9783764361587)
DOI
10.1007/b11797
Schweitzer Classification
Content
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.