ABSTRACT

Combinatorics of Spreads and Parallelisms covers all known finite and infinite parallelisms as well as the planes comprising them. It also presents a complete analysis of general spreads and partitions of vector spaces that provide groups enabling the construction of subgeometry partitions of projective spaces.The book describes general partitions

part |2 pages

Part 1. Partitions of Vector Spaces

chapter 1|12 pages

Quasi-subgeometry Partitions

chapter 2|28 pages

Finite Focal-Spreads

chapter 3|18 pages

Generalizing André Spreads

part |2 pages

Part 2. Subgeometry Partitions

chapter 6|8 pages

Subgeometries from Focal-Spreads

chapter 7|6 pages

Extended André Subgeometries

chapter 8|14 pages

Kantor’s Flag-Transitive Designs

chapter 9|14 pages

Maximal Additive Partial Spreads

part |2 pages

Part 3. Subplane Covered Nets and Baer Groups

chapter 10|14 pages

Partial Desarguesian t-Parallelisms

chapter 11|14 pages

Direct Products of A¢ ne Planes

chapter 12|8 pages

Jha-Johnson SL(2; q) C-Theorem

chapter 13|32 pages

Baer Groups of Nets

chapter 14|20 pages

Ubiquity of Subgeometry Partitions

part |2 pages

Part 4. Flocks and Related Geometries

chapter 15|14 pages

Spreads Covered by Pseudo-Reguli

chapter 16|22 pages

Flocks

chapter 17|14 pages

Regulus-Inducing Homology Groups

chapter 18|6 pages

Hyperbolic Fibrations and Partial Flocks

chapter 19|12 pages

j-Planes and Monomial Flocks

part |2 pages

Part 5. Derivable Geometries

chapter 20|14 pages

Flocks of -Cones

chapter 21|12 pages

Parallelisms of Quadric Sets

chapter 22|14 pages

Sharply k-Transitive Sets

chapter 23|18 pages

Transversals to Derivable Nets

chapter 24|20 pages

Partially Flag-Transitive A¢ ne Planes

chapter 25|4 pages

Special Topics on Parallelisms

part |2 pages

Part 6. Constructions of Parallelisms

chapter 26|16 pages

Regular Parallelisms

chapter 28|20 pages

Johnson Partial Parallelisms

chapter |4 pages

Part 7. Parallelism-Inducing Groups

chapter 31|40 pages

General Parallelism-Inducing Groups

part |2 pages

Part 8. Coset Switching

chapter 32|16 pages

Finite E-Switching

chapter 33|8 pages

Parallelisms over Ordered Fields

chapter 34|14 pages

General Elation Switching

chapter 35|14 pages

Dual Parallelisms

part |2 pages

Part 9. Transitivity

chapter 36|10 pages

p-Primitive Parallelisms

chapter 37|6 pages

Transitive t-Parallelisms

chapter 38|22 pages

Transitive Deficiency One

chapter 39|8 pages

Doubly Transitive Focal-Spreads

part |2 pages

Part 10. Appendices

chapter 40|16 pages

Open Problems

chapter 41|4 pages

Geometry Background

chapter 42|4 pages

The Klein Quadric

chapter 43|14 pages

Major Theorems of Finite Groups

chapter 44|2 pages

The Diagram