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By Gunter Malle
By Donna Testerman
Publisher: Cambridge University Press
Print Publication Year:2011
Online Publication Date:June 2012
Online ISBN:9780511994777
Hardback ISBN:9781107008540
Paperback ISBN:9781107471443
Book DOI: http://dx.doi.org/10.1017/CBO9780511994777
Subjects: Algebra
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.
Reviews:
pp. i-iv
pp. v-viii
pp. ix-xii
pp. xiii-xiii
pp. xiv-xiv
PART I - LINEAR ALGEBRAIC GROUPS: Read PDF
pp. 1-2
pp. 3-14
2 - Jordan decomposition: Read PDF
pp. 15-19
3 - Commutative linear algebraic groups: Read PDF
pp. 20-25
4 - Connected solvable groups: Read PDF
pp. 26-29
5 - G-spaces and quotients: Read PDF
pp. 30-35
pp. 36-43
7 - The Lie algebra of a linear algebraic group: Read PDF
pp. 44-50
8 - Structure of reductive groups: Read PDF
pp. 51-62
9 - The classification of semisimple algebraic groups: Read PDF
pp. 63-73
10 - Exercises for Part I: Read PDF
pp. 74-80
PART II - SUBGROUP STRUCTURE AND REPRESENTATION THEORY OF SEMISIMPLE ALGEBRAIC GROUPS: Read PDF
pp. 81-82
11 - BN-pairs and Bruhat decomposition: Read PDF
pp. 83-94
12 - Structure of parabolic subgroups, I: Read PDF
pp. 95-103
13 - Subgroups of maximal rank: Read PDF
pp. 104-111
14 - Centralizers and conjugacy classes: Read PDF
pp. 112-120
15 - Representations of algebraic groups: Read PDF
pp. 121-130
16 - Representation theory and maximal subgroups: Read PDF
pp. 131-139
17 - Structure of parabolic subgroups, II: Read PDF
pp. 140-148
18 - Maximal subgroups of classical type simple algebraic groups: Read PDF
pp. 149-165
19 - Maximal subgroups of exceptional type algebraic groups: Read PDF
pp. 166-171
20 - Exercises for Part II: Read PDF
pp. 172-178
PART III - FINITE GROUPS OF LIE TYPE: Read PDF
pp. 179-180
21 - Steinberg endomorphisms: Read PDF
pp. 181-187
22 - Classification of finite groups of Lie type: Read PDF
pp. 188-196
23 - Weyl group, root system and root subgroups: Read PDF
pp. 197-202
24 - A BN-pair for GF : Read PDF
pp. 203-217
25 - Tori and Sylow subgroups: Read PDF
pp. 218-228
26 - Subgroups of maximal rank: Read PDF
pp. 229-235
27 - Maximal subgroups of finite classical groups: Read PDF
pp. 236-243
28 - About the classes and S : Read PDF
pp. 244-249
29 - Exceptional groups of Lie type: Read PDF
pp. 250-262
30 - Exercises for Part III: Read PDF
pp. 263-267
Appendix A - Root systems: Read PDF
pp. 268-281
Appendix B - Subsystems: Read PDF
pp. 282-296
Appendix C - Automorphisms of root systems: Read PDF
pp. 297-300
pp. 301-304
pp. 305-309