Translation Planes /

Translation Planes / by Heinz Lüneburg.

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Lüneburg, Heinz
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 1980.
Subjects:
Mathematics.
Geometry.
Table of Contents:
  • 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 Doubly Transitively 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.

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