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Handbook of Finite Translation Planes

Handbook of Finite Translation Planes by Norman Johnson
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Preface and Acknowledgments
An Overview
Translation Plane Structure Theory
Partial Spreads and Translation Nets
Partial Spreads and Generalizations
Frequently Used Tools
Sharply Transitive Sets
SL(2, p) × SL(2, p)-Planes
Classical Semifields
Groups of Generalized Twisted Field Planes
Nuclear Fusion in Semifields
Cyclic Semifields
T-Cyclic GL(2, q)-Spreads
Cone Representation Theory
André Net Replacements and Ostrom-Wilke Generalizations
Foulser's ?-Planes
Regulus Lifts, Intersections over Extension Fields
Hyper-Reguli Arising from André Hyper-Reguli
Translation Planes with Large Homology Groups
Derived Generalized André Planes
The Classes of Generalized André Planes
C-System Nearfields
Subregular Spreads
Fano Configurations
Fano Configurations in Generalized André Planes
Planes with Many Elation Axes
Klein Quadric
Transitive Parallelisms
Known Ovoids
Simple T-Extensions of Derivable Nets
Baer Groups on Parabolic Spreads
Algebraic Lifting
Semifield Planes of Orders q4, q6
Known Classes of Semifields
Methods of Oyama and the Planes of Suetake
Coupled Planes
Subgeometry Partitions
Groups on Multiple Hyper-Reguli
Hyper-Reguli of Dimension 3
Elation-Baer Incompatibility
Hering-Ostrom Elation Theorem
Baer-Elation Theory
Spreads Admitting Unimodular Sections-Foulser-Johnson Theorem
Spreads of Order q2-Groups of Order q2
Transversal Extensions
Indicator Sets
Geometries and Partitions
Maximal Partial Spreads
Sperner Spaces
Conical Flocks
Ostrom and Flock Derivation
Transitive Skeletons
BLT-Set Examples
Many Ostrom-Derivates
Infinite Classes of Flocks
Sporadic Flocks
Hyperbolic Fibrations
Spreads with Many Homologies
Nests of Reguli
Multiple Nests
A Few Remarks on Isomorphisms
Flag-Transitive Geometries
Quartic Groups in Translation Planes
Double Transitivity
Triangle Transitive Planes
Hiramine-Johnson-Draayer Theory
Bol Planes
2/3-Transitive Axial Groups
Doubly Transitive Ovals and Unitals
Rank 3 Affine Planes
Transitive Extensions
Higher-Dimensional Flocks
Orthogonal Spreads
Symplectic Groups-The Basics
Symplectic Flag-Transitive Spreads
Symplectic Spreads
When Is a Spread Not Symplectic?
When Is a Spread Symplectic?
The Translation Dual of a Semifield
Unitals in Translation Planes
Hyperbolic Unital Groups
Transitive Parabolic Groups
Doubly Transitive Hyperbolic Unital Groups
Multiple Spread Retraction
Transitive Baer Subgeometry Partitions
Geometric and Algebraic Lifting
Quasi-Subgeometry Partitions
Hyper-Regulus Partitions
Small-Order Translation Planes
Dual Translation Planes and Their Derivates
Affine Planes with Transitive Groups
Cartesian Group Planes-Coulter-Matthews
Planes Admitting PGL(3, q)
Planes of Order = 25
Real Orthogonal Groups and Lattices
Aspects of Symplectic and Orthogonal Geometry
Fundamental Results on Groups
Atlas of Planes and Processes
General Index
CRC Press; February 2007
884 pages; ISBN 9781420011142
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Title: Handbook of Finite Translation Planes
Author: Norman Johnson; Vikram Jha; Mauro Biliotti
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