Handbook of Finite Translation Planes
eBook - ePub

Handbook of Finite Translation Planes

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

Handbook of Finite Translation Planes

About this book

The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of Andre to coordi

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Yes, you can access Handbook of Finite Translation Planes by Norman Johnson,Vikram Jha,Mauro Biliotti in PDF and/or ePUB format, as well as other popular books in Mathematics & Counting & Numeration. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half Title
  3. Pure And Applied Mathematics
  4. Monographs And Textbooks In Pure And Applied Mathematics
  5. Copyright Page
  6. Dedication
  7. Table of Contents
  8. Preface and Acknowledgments.
  9. 1 An Overview.
  10. 2 Translation Plane Structure Theory.
  11. 3 Partial Spreads and Translation Nets.
  12. 4 Partial Spreads and Generalizations.
  13. 5 Quasifields.
  14. 6 Derivation.
  15. 7 Frequently Used Tools.
  16. 8 Sharply Transitive Sets.
  17. 9 SL(2,p)×SL(2,p)-Planes.
  18. 10 Classical Semifields.
  19. 11 Groups of Generalized Twisted Field Planes.
  20. 12 Nuclear Fusion in Semifields.
  21. 13 Cyclic Semifields.
  22. 14 T-Cyclic GL(2,q)-Spreads.
  23. 15 Cone Representation Theory.
  24. 16 André Net Replacements and Ostrom-Wilke Generalizations.
  25. 17 Foulser’s λ-Planes.
  26. 18 Regulus Lifts, Intersections over Extension Fields.
  27. 19 Hyper-Reguli Arising from André Hyper-Reguli.
  28. 20 Translation Planes with Large Homology Groups.
  29. 21 Derived Generalized André Planes.
  30. 22 The Classes of Generalized André Planes.
  31. 23 C-System Nearfields.
  32. 24 Subregular Spreads.
  33. 25 Fano Configurations.
  34. 26 Fano Configurations in Generalized André Planes.
  35. 27 Planes with Many Elation Axes.
  36. 28 Klein Quadric.
  37. 29 Parallelisms.
  38. 30 Transitive Parallelisms.
  39. 31 Ovoids.
  40. 32 Known Ovoids.
  41. 33 Simple T-Extensions of Derivable Nets.
  42. 34 Baer Groups on Parabolic Spreads.
  43. 35 Algebraic Lifting.
  44. 36 Semifield Planes of Orders q4,q6.
  45. 37 Known Classes of Semifields.
  46. 38 Methods of Oyama, and the Planes of Suetake.
  47. 39 Coupled Planes.
  48. 40 Hyper-Reguli.
  49. 42 Groups on Multiple Hyper-Reguli.
  50. 43 Hyper-Reguli of Dimension 3.
  51. 44 Elation-Baer Incompatibility.
  52. 45 Hering-Ostrom Elation Theorem.
  53. 46 Baer Elation Theory.
  54. 47 Spreads Admitting Unimodular Sections-Foulser-Johnson Theorem.
  55. 48 Spreads of Order q2 —Groups of Order q2.
  56. 49 Transversal Extensions.
  57. 50 Indicator Sets.
  58. 51 Geometries and Partitions.
  59. 52 Maximal Partial Spreads.
  60. 53 Sperner Spaces.
  61. 54 Conical Flocks.
  62. 55 Ostrom and Flock Derivation.
  63. 56 Transitive Skeletons.
  64. 57 BLT-Set Examples.
  65. 58 Many Ostrom-Derivates.
  66. 59 Infinite Classes of Flocks.
  67. 60 Sporadic Flocks.
  68. 61 Hyperbolic Fibrations.
  69. 62 Spreads with 'Many' Homologies.
  70. 63 Nests of Reguli.
  71. 64 Chains.
  72. 65 Multiple Nests.
  73. 66 A Few Remarks on Isomorphisms.
  74. 67 Flag-Transitive Geometries.
  75. 68 Quartic Groups in Translation Planes.
  76. 69 Double Transitivity.
  77. 70 Triangle Transitive Planes.
  78. 71 Hiramine-Johnson-Draayer Theory.
  79. 72 Bol Planes.
  80. 73 2/3-Transitive Axial Groups.
  81. 74 Doubly Transitive Ovals and Unitals.
  82. 75 Rank 3 Affine Planes.
  83. 76 Transitive Extensions.
  84. 77 Higher-Dimensional Flocks
  85. 78 j...j-Planes
  86. 79 Orthogonal Spreads
  87. 80 Symplectic Groups-The Basics
  88. 81 Symplectic Flag-Transitive Spreads
  89. 82 Symplectic Spreads
  90. 83 When Is a Spread Not Symplectic?.....
  91. 84 When Is a Spread Symplectic?.....
  92. 85 The Translation Dual of a Semifield
  93. 86 Unitals in Translation Planes
  94. 87 Hyperbolic Unital Groups
  95. 88 Transitive Parabolic Groups
  96. 89 Doubly Transitive Hyperbolic Unital Groups
  97. 90 Retraction
  98. 91 Multiple Spread Retraction
  99. 92 Transitive Baer Subgeometry Partitions
  100. 93 Geometric and Algebraic Lifting
  101. 94 Quasi-Subgeometry Partitions
  102. 95 Hyper-Regulus Partitions
  103. 96 Small-Order Translation Planes
  104. 97 Dual Translation Planes and Their Derivates
  105. 98 Affine Planes with Transitive Groups
  106. 99 Cartesian Group Planes-Coulter-Matthews
  107. 100 Planes Admitting PGL(3,q)
  108. 101 Planes of Order ≀25
  109. 102 Real Orthogonal Groups and Lattices.
  110. 103 Aspects of Symplectic and Orthogonal Geometry.
  111. 104 Fundamental Results on Groups.
  112. 105 Atlas of Planes and Processes.
  113. Bibliography
  114. Theorems
  115. Index
  116. General Index