Contents
List of Tables xi
Preface xiii
PART I, CHAPTER A: ALMOST SIMPLE K-GROUPS
Chapter 1. Some Theory of Linear Algebraic Groups 1
1.1. Fundamental Notions 2
1.2. Jordan Decomposition 4
1.3. Unipotent Groups; One-Parameter Groups 5
1.4. Tori 6
1.5. Solvable Algebraic Groups 6
1.6. Borel Subgroups 7
1.7. Radical; Reductive, Semisimple and Simple Groups 7
1.8. Abstract Root Systems 8
1.9. Weights, Roots and Root Subgroups in Reductive Groups 13
1.10. Classification of Semisimple Groups; Isogenics and Versions 15
1.11. £iV-Structure 16
1.12. Chevalley Generators and Relations 17
1.13. Parabolic Subgroups 22
1.14. Weights and Representations 23
1.15. Isomorphisms, Automorphisms and Endomorphisms 27
1.16. Notes 30
Chapter 2. The Finite Groups of Lie Type 31
2.1. Steinberg Endomorphisms and Lang's Theorem 31
2.2. The Finite Groups of Lie Type 36
2.3. Bruhat Structure 40
2.4. Chevalley Relations for Finite Groups of Lie Type 45
2.5. Automorphisms 53
2.6. Subsystem Subgroups and Parabolic Subgroups 63
2.7. The Classical Groups 67
2.8. Equicharacteristic Representations 73
2.9. Presentations; Curtis-Tits Theorem 79
2.10. Standard Notation 89
Chapter 3. Local Subgroups of Groups of Lie Type, I 91
3.1. A Theorem of Borel and Tits 91
3.2. Structure of Parabolic Subgroups 95
3.3. Equicharacteristic Sylow Structure 106
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