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＜電子ブック＞
Symmetry in Finite Generalized Quadrangles / by Koen Thas
(Frontiers in Mathematics. ISSN:16608054)

版	1st ed. 2004.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2004
本文言語	英語
大きさ	XXI, 214 p : online resource
著者標目	*Thas, Koen author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Convex geometry  LCSH:Discrete geometry FREE:Geometry FREE:Convex and Discrete Geometry
一般注記	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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