Author | Thas, Koen. author |
---|---|

Title | Symmetry in Finite Generalized Quadrangles [electronic resource] / by Koen Thas |

Imprint | Basel : Birkhรคuser Basel, 2004 |

Connect to | http://dx.doi.org/10.1007/b11797 |

Descript | XXI, 214 p. online resource |

SUMMARY

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

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

Mathematics
Geometry
Convex geometry
Discrete geometry
Mathematics
Geometry
Convex and Discrete Geometry