ABSTRACT

An exploration of the construction and analysis of translation planes to spreads, partial spreads, co-ordinate structures, automorphisms, autotopisms, and collineation groups. It emphasizes the manipulation of incidence structures by various co-ordinate systems, including quasisets, spreads and matrix spreadsets. The volume showcases methods of str

chapter 1|8 pages

An Overview

chapter 2|16 pages

Andre’s Theory of Spreads

2.1 Introduction

chapter 3|14 pages

Spreads in PG(3,K)

3.1 Introduction

chapter 4|20 pages

Partial Spreads and Translation Nets

4.1 Introduction

chapter 5|10 pages

Spreadsets and Partial Spreadsets

5.1 Introduction

chapter 6|26 pages

Geometry of Spreadsets: V(r)

6.1 Introduction

chapter 7|24 pages

Coordinatization by Spreadsets: General Cases

7.1 Introduction

chapter 8|16 pages

Partial Quasifields

8.1 Introduction

chapter 9|20 pages

Coordinatization by (Partial) Quasifields

9.1 Introduction

chapter 10|8 pages

Rational Desarguesian Nets

10.1 Introduction

chapter 11|12 pages

Quasigroups, Loops and Nuclei

11.1 Introduction

chapter 12|40 pages

(Pre)Quasifields: Algebraic Axioms and Autotopisms

12.1 Introduction

chapter 13|14 pages

The Kernel of Spreadsets and Quasifields

13.1 Introduction Hom(y,+)that leaves invariant every component. By the Andre theory

chapter 14|14 pages

Quadratics of Two-Dimensional Quasifields: Hall Systems

14.1 Introduction

chapter 15|12 pages

Spreads in Projective Spaces

15.1 Introduction

chapter 16|8 pages

Kernel Subplanes across Desarguesian Nets

16.1 Introduction

chapter 17|12 pages

Derivation of Finite Spreads

17.1 Introduction

chapter 18|8 pages

Foulser’s Covering Theorem

18.1 Introduction

chapter 19|14 pages

Structure of Baer Groups

19.1 Introduction

chapter 21|12 pages

Large Planar Groups

21.1 Introduction

chapter 22|22 pages

Finite Generalized Andre Systems and Nearfields

22.1 Introduction

chapter 23|22 pages

Elation Net Theory

23.1 Algebra Generated by a Matrix A

chapter 24|22 pages

Baer-Elation Theory

24.1 Introduction

chapter 25|18 pages

Semifields

25.1 Introduction

chapter 26|14 pages

Simple T-Extensions of Derivable Nets

26.1 Introduction

chapter 27|6 pages

Cyclic Semifields

27.1 Intro duction

chapter 28|16 pages

Baer Groups on Parabolic Spreads

28.1 Introduction

chapter 29|30 pages

Lifting and Quasifibrations

29.1 Introduction

chapter 30|14 pages

Mixed Tangentially Transitive Planes

30.1 Introduction

chapter 31|8 pages

Maximal Partial Spreads

31.1 Introduction

chapter 32|10 pages

Foulser-Johnson SL(2, g)-Theorem

SL(2, 32,1 Introduction