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AuthorLรผneburg, Heinz. author
TitleTranslation Planes [electronic resource] / by Heinz Lรผneburg
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1980
Connect tohttp://dx.doi.org/10.1007/978-3-642-67412-9
Descript X, 278 p. online resource

CONTENT

I Introduction -- 1. Andrรฉโ{128}{153}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 Andrรฉ Planes -- 6. Some Number Theoretic Tools -- 7. Finite Nearfield Planes -- 8. The Nearfield Plane of Order 9 -- 9. Generalized Andrรฉ Planes -- 10. Finite Generalized Andrรฉ Planes -- 11. Homologies of Finite Generalized Andrรฉ Planes -- 12. The Andrรฉ Planes -- 13. The Hall Planes -- 14. The Collineation Group of a Generalized Andrรฉ 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 Lรผneburg Planes -- 24. The Subgroups of the Suzuki Groups -- 25. Mรถbius Planes -- 26. The Mรถbius 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 Lรผneburg 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 Schรคffer 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 Schรคffer Planes -- 51. The Theorem of Cofman-Prohaska -- 52. Prohaskaโ{128}{153}s Characterization of the Hall Planes -- Index of Special Symbols


Mathematics Geometry Mathematics Geometry



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