ABSTRACT

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

chapter 1|4 pages

An Overview

chapter 2|8 pages

Translation Plane Structure Theory

chapter 3|4 pages

Partial Spreads and Translation Nets

chapter 4|12 pages

Partial Spreads and Generalizations

chapter 5|18 pages

Quasifields

chapter 6|8 pages

Derivation

chapter 7|4 pages

Frequently Used Tools

chapter 8|4 pages

Sharply Transitive Sets

chapter 9|8 pages

SL(2, p)× SL(2, p)-Planes

chapter 10|6 pages

Classical Semifields

chapter 11|14 pages

Groups of Generalized Twisted Field Planes

chapter 12|18 pages

Nuclear Fusion in Semifields

chapter 13|4 pages

Cyclic Semifields

chapter 14|4 pages

T -Cyclic GL(2, q)-Spreads

chapter 15|6 pages

Cone Representation Theory

chapter 17|12 pages

Foulser’s λ-Planes

chapter 18|10 pages

Regulus Lifts, Fields

chapter 21|4 pages

Derived Generalized Andre´ Planes

chapter 22|2 pages

The Classes of Generalized Andre´ Planes

chapter 23|4 pages

C-System Nearfields

chapter 24|36 pages

Subregular Spreads

chapter 25|6 pages

Fano Configurations

chapter 27|4 pages

Planes with Many Elation Axes

chapter 28|2 pages

Klein Quadric

chapter 29|10 pages

Parallelisms

chapter 30|6 pages

Transitive Parallelisms

chapter 31|4 pages

Ovoids

chapter 32|4 pages

Known Ovoids

chapter 33|8 pages

Simple T -Extensions of Derivable Nets

chapter 34|6 pages

Baer Groups on Parabolic Spreads

chapter 35|8 pages

Algebraic Lifting

chapter 36|6 pages

Semifield Planes of Orders q4, q6

chapter 37|6 pages

Known Classes of Semifields

chapter 39|8 pages

Coupled Planes

chapter 40|10 pages

Hyper-Reguli

chapter 41|4 pages

Subgeometry Partitions

chapter 42|4 pages

Groups on Multiple Hyper-Reguli

chapter 43|8 pages

Hyper-Reguli of Dimension 3

chapter 44|6 pages

Elation-Baer Incompatibility

chapter 45|4 pages

Hering–Ostrom Elation Theorem

chapter 46|4 pages

Baer Elation Theory

chapter 48|6 pages

Spreads of Order q2—Groups of Order q2

chapter 49|16 pages

Transversal Extensions

chapter 50|20 pages

Indicator Sets

chapter 51|12 pages

Geometries and Partitions

chapter 52|2 pages

Maximal Partial Spreads

chapter 53|2 pages

Sperner Spaces

chapter 54|12 pages

Conical Flocks

chapter 55|10 pages

Ostrom and Flock Derivation

chapter 56|2 pages

Transitive Skeletons

chapter 57|4 pages

BLT -Set Examples

chapter 58|2 pages

Many Ostrom-Derivates

chapter 59|6 pages

Infinite Classes of Flocks

chapter 60|4 pages

Sporadic Flocks

chapter 61|12 pages

Hyperbolic Fibrations

chapter 62|10 pages

Spreads with ‘Many’ Homologies

chapter 63|14 pages

Nests of Reguli

chapter 64|6 pages

Chains

chapter 65|10 pages

Multiple Nests

chapter 66|2 pages

A Few Remarks on Isomorphisms

chapter 67|6 pages

Flag-Transitive Geometries

chapter 68|6 pages

Quartic Groups in Translation Planes

chapter 69|6 pages

Double Transitivity

chapter 70|2 pages

Triangle Transitive Planes

chapter 71|6 pages

Hiramine–Johnson–Draayer Theory

chapter 72|2 pages

Bol Planes

chapter 73|4 pages

2/3-Transitive Axial Groups

chapter 74|4 pages

Doubly Transitive Ovals and Unitals

chapter 75|4 pages

Rank 3 Affine Planes

chapter 76|12 pages

Transitive Extensions

chapter 77|14 pages

Higher-Dimensional Flocks

chapter 78|14 pages

j. . . j-Planes

chapter 79|6 pages

Orthogonal Spreads

chapter 80|8 pages

Symplectic Groups—The Basics

chapter 81|22 pages

Symplectic Flag-Transitive Spreads

chapter 82|12 pages

Symplectic Spreads

chapter 83|10 pages

When Is a Spread Not Symplectic?

chapter 84|2 pages

When Is a Spread Symplectic?

chapter 85|6 pages

The Translation Dual of a Semifield

chapter 86|12 pages

Unitals in Translation Planes

chapter 87|10 pages

Hyperbolic Unital Groups

chapter 88|2 pages

Transitive Parabolic Groups

chapter 89|4 pages

Doubly Transitive Groups

chapter 90|16 pages

Retraction

chapter 91|8 pages

Multiple Spread Retraction

chapter 92|8 pages

Transitive Baer Subgeometry Partitions

chapter 93|6 pages

Geometric and Algebraic Lifting

chapter 94|16 pages

Quasi-Subgeometry Partitions

chapter 95|6 pages

Hyper-Regulus Partitions

chapter 96|8 pages

Small-Order Translation Planes

chapter 98|2 pages

Affine Planes with Transitive Groups

chapter 100|2 pages

Planes Admitting PGL(3, q)

chapter 101|2 pages

Planes of Order…

chapter 102|4 pages

Real Orthogonal Groups and Lattices

chapter 103|18 pages

Aspects of Symplectic and Orthogonal Geometry

chapter 104|8 pages

Fundamental Results on Groups

chapter 105|18 pages

Atlas of Planes and Processes