Translation Planes

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.