Preface
List of tables
Notation
Part I. Linear Algebraic Groups:
1. Basic concepts
2. Jordan decomposition
3. Commutative linear algebraic groups
4. Connected solvable groups
5. G-spaces and quotients
6. Borel subgroups
7. The Lie algebra of a linear algebraic group
8. Structure of reductive groups
9. The classification of semisimple algebraic groups
10. Exercises for Part I
Part II. Subgroup Structure and Representation Theory of Semisimple Algebraic Groups:
11. BN-pairs and Bruhat decomposition
12. Structure of parabolic subgroups, I
13. Subgroups of maximal rank
14. Centralizers and conjugacy classes
15. Representations of algebraic groups
16. Representation theory and maximal subgroups
17. Structure of parabolic subgroups, II
18. Maximal subgroups of classical type simple algebraic groups
19. Maximal subgroups of exceptional type algebraic groups
20. Exercises for Part II
Part III. Finite Groups of Lie Type:
21. Steinberg endomorphisms
22. Classification of finite groups of Lie type
23. Weyl group, root system and root subgroups
24. A BN-pair for GF
25. Tori and Sylow subgroups
26. Subgroups of maximal rank
27. Maximal subgroups of finite classical groups
28. About the classes CF1, …, CF7 and S
29. Exceptional groups of Lie type
30. Exercises for Part III
Appendix A. Root systems
Appendix B. Subsystems
Appendix C. Automorphisms of root systems
References
Index.
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