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Symmetry in Finite Generalized Quadrangles / by Koen Thas
(Frontiers in Mathematics. ISSN:16608054)
Edition | 1st ed. 2004. |
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Publisher | (Basel : Birkhäuser Basel : Imprint: Birkhäuser) |
Year | 2004 |
Language | English |
Size | XXI, 214 p : online resource |
Authors | *Thas, Koen author SpringerLink (Online service) |
Subjects | LCSH:Geometry LCSH:Convex geometry LCSH:Discrete geometry FREE:Geometry FREE:Convex and Discrete Geometry |
Notes | 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 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 HTTP:URL=https://doi.org/10.1007/b11797 |
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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | オンライン | 電子ブック |
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Springer eBooks | 9783764377977 |
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EB00232313 |
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