Handbook of Finite Translation Planes
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A01=Mauro Biliotti
A01=Norman Johnson
A01=Vikram Jha
advanced translation plane classification
affine
Affine Desarguesian Plane
Affine Homology Group
Affine Plane
algebraic structures in mathematics
Author_Mauro Biliotti
Author_Norman Johnson
Author_Vikram Jha
automorphisms
baer
Baer Group
Baer Subplanes
Category=PBM
collineation
Collineation Group
combinatorial design
Conical Flock Plane
Derivable Nets
desarguesian
desarguesian nets
Desarguesian Plane
Desarguesian Spread
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
finite geometry
Finite Translation Planes
Generalized Twisted Field Planes
geometry
group
group actions in geometry
Homology Group
Hyperbolic Quadrics
Irregular Nearfield Planes
Kernel Homology Group
Nearfield Planes
Norman Johnson
order
Order Q2
Order Qn
partial
Partial Spread
plane structure theory
projective planes
quadrangles
Quadratic Cones
quadric sets
quasifield theory
Regulus Net
semifield
Semifield Plane
Semifield Spread
spread
subplane
Translation Planes
Product details
- ISBN 9781584886051
- Weight: 1344g
- Dimensions: 174 x 246mm
- Publication Date: 15 Feb 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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 André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes.
As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples.
Norman Johnson, Vikram Jha, Mauro Biliotti
