Lüneburg Translation Planes

1980
ISBN: 978-3-642-67412-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 278 Seiten, eBook

Zielgruppe

Research

Autoren/Hrsg.

Lüneburg, H.

Inhaltsverzeichnis

I Introduction.- 1. André’s Description of Translation Planes.- 2. An Alternative Description of Translation Planes.- 3. Homologies and Shears of Translation Planes.- 4. A Characterization of Pappian Planes.- 5. Quasifields.- II Generalized André Planes.- 6. Some Number Theoretic Tools.- 7. Finite Nearfield Planes.- 8. The Nearfield Plane of Order 9.- 9. Generalized André Planes.- 10. Finite Generalized André Planes.- 11. Homologies of Finite Generalized André Planes.- 12. The André Planes.- 13. The Hall Planes.- 14. The Collineation Group of a Generalized André Plane.- III Rank-3-Planes.- 15. Line Transitive Affine Planes.- 16. Affine Planes of Rank 3.- 17. Rank-3-Planes with an Orbit of Length 2 on the Line at Infinity.- 18. The Planes of Type R*p.- 19. The Planes of Type F*p.- 20. Exceptional Rank-3-Planes.- IV The Suzuki Groups and Their Geometries.- 21. The Suzuki Groups S(K,?).- 22. The Simplicity of the Suzuki Groups.- 23. The Lüneburg Planes.- 24. The Subgroups of the Suzuki Groups.- 25. Möbius Planes.- 26. The Möbius Planes Belonging to the Suzuki Groups.- 27. S(q) as a Collineation Group of PG(3, q).- 28. S(q) as a Collineation Group of a Plane of Order q2.- 29. Geometric Partitions.- 30. Rank-3-Groups.- 31. A Characterization of the Lüneburg Planes.- V Planes Admitting Many Shears.- 32. Unitary Polarities of Finite Desarguesian Projective Planes and Their Centralizers.- 33. A Characterization of A5.- 34. A Characterization of Galois Fields of Odd Characteristic.- 35. Groups Generated by Shears.- VI Flag Transitive Planes.- 36. The Uniqueness of the Desarguesian Plane of Order 8.- 37. Soluble Flag Transitive Collineation Groups.- 38. Some Characterizations of Finite Desarguesian Planes.- 39. Translation Planes Whose Collineation Group Acts DoublyTransitively on l?.- 40. A Theorem of Burmester and Hughes.- 41. Bol Planes.- VII Translation Planes of Order q2 Admitting SL(2, q) as a Collineation Group.- 42. Ovals in Finite Desarguesian Planes.- 43. Twisted Cubics.- 44. Irreducible Representations of SL(2,2r).- 45. The Hering and the Schäffer Planes.- 46. Three Planes of Order 25.- 47. Quasitransvections.- 48. Desarguesian Spreads in V(4, q).- 49. Translation Planes of Order q2 Admitting SL(2, q) as a Collineation Group.- 50. The Collineation Groups of the Hering and Schäffer Planes.- 51. The Theorem of Cofman-Prohaska.- 52. Prohaska’s Characterization of the Hall Planes.- Index of Special Symbols.