Linear algebraic groups and finite groups of lie type
 Responsibility
 Gunter Malle, Donna Testerman.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge Univ Press, 2011.
 Physical description
 xii, 309 p. : ill. ; 24 cm.
 Series
 Cambridge studies in advanced mathematics ; 133.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA179 .M35 2011  Unknown 
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Creators/Contributors
 Author/Creator
 Malle, Gunter.
 Contributor
 Testerman, Donna M., 1960
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [301]304) and index.
 Contents

 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. Gspaces 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. BNpairs 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 BNpair 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 Originating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2011
 Series
 Cambridge studies in advanced mathematics ; 133
 ISBN
 1107008549 (hardback)
 9781107008540 (hardback)