The classification of the finite simple groups: Number 3 Part I, Chapter A: Almost simple K-groups
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1998]
|
| Series: | Mathematical surveys and monographs
Volume 40,3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 419 Seiten |
| ISBN: | 0821803913 9780821803912 |
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MARC
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| 245 | 1 | 0 | |a The classification of the finite simple groups |n Number 3 |p Part I, Chapter A: Almost simple K-groups |c Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1998] | |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 40,3 | |
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Record in the Search Index
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Contents
List of Tables xi
Preface xiii
PART I, CHAPTER A: ALMOST SIMPLE 3C 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; Isogenies and Versions 15
1.11. BiV 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
ix
x CONTENTS
Chapter 4. Local Subgroups of Groups of Lie Type, II 119
4.1. Semisimple Automorphisms of Algebraic Groups 119
4.2. Semisimple Automorphisms of Finite Groups of Lie Type 134
4.3. Centralizers of Involutions in Aut0(K): Statements 143
4.4. Centralizers of Involutions in Auto{K): Proofs 153
4.5. Centralizers of Involutions in Groups in Lie(r), r Odd: Statements 170
4.6. Centralizers of Involutions in Groups in Lie{r), r Odd: Proofs 186
4.7. Inner Diagonal and Graph Automorphisms of Exceptional Odd
Prime Orders 204
4.8. Some Other p Local Subgroups 219
4.9. The Remaining Types of Non Inner Automorphisms 227
4.10. Cross Characteristic Sylow Structure 236
Chapter 5. The Alternating Groups and the Twenty Six Sporadic
Groups 249
5.1. Schur Multipliers and Coverings of Simple Groups 249
5.2. The Alternating Groups 252
5.3. Structure of the Twenty Six Sporadic Groups 259
5.4. Justification of the Tables: The Simple Case 288
5.5. Justification of the Tables: The Non Simple Case 294
5.6. Ranks of Sporadic Groups 302
Chapter 6. Coverings and Embeddings of Quasisimple 3C Groups 311
6.1. The Schur Multipliers and Covering Groups of the Simple
K Groups 311
6.2. Some Embeddings of Quasisimple Groups 313
6.3. The Action of Out(K) on M{K) 317
6.4. Splitting and Stable Involutions 324
6.5. Subgroups of Small Simple Groups 328
Chapter 7. General Properties of DC Groups 335
7.1. Verification of the Fundamental DC Group Properties 335
7.2. Generation of Semisimple Groups: Generalities 343
7.3. Generation for Groups in Shev: Statements of Main Results 346
7.4. Generation for Groups in Shev: Proofs 349
7.5. Generation for Groups in Alt U Spar 380
7.6. Strongly p Embedded Subgroups and Proper fc Generated Cores 383
7.7. Balance and Signalizers 385
7.8. Fusion 399
Background References 403
Expository References 404
Errata for Numbers 1 and 2 409
Glossary 410
Index 414 |
| any_adam_object | 1 |
| author | Gorenstein, Daniel 1923-1992 Lyons, Richard 1945- Solomon, Ronald 1948- |
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| illustrated | Not Illustrated |
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| isbn | 0821803913 9780821803912 |
| language | English |
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| physical | xv, 419 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| series2 | Mathematical surveys and monographs |
| spelling | Gorenstein, Daniel 1923-1992 Verfasser (DE-588)1077470711 aut The classification of the finite simple groups Number 3 Part I, Chapter A: Almost simple K-groups Daniel Gorenstein ; Richard Lyons ; Ronald Solomon Providence, Rhode Island American Mathematical Society [1998] xv, 419 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 40,3 Mathematical surveys and monographs Groupes simples finis ram Finite simple groups Lyons, Richard 1945- Verfasser (DE-588)172234360 aut Solomon, Ronald 1948- Verfasser (DE-588)1011397684 aut (DE-604)BV010647435 3 Erscheint auch als Online-Ausgabe 978-1-4704-1268-5 Mathematical surveys and monographs Volume 40,3 (DE-604)BV000018014 40,3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010176946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gorenstein, Daniel 1923-1992 Lyons, Richard 1945- Solomon, Ronald 1948- The classification of the finite simple groups Mathematical surveys and monographs Groupes simples finis ram Finite simple groups |
| title | The classification of the finite simple groups |
| title_auth | The classification of the finite simple groups |
| title_exact_search | The classification of the finite simple groups |
| title_full | The classification of the finite simple groups Number 3 Part I, Chapter A: Almost simple K-groups Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| title_fullStr | The classification of the finite simple groups Number 3 Part I, Chapter A: Almost simple K-groups Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| title_full_unstemmed | The classification of the finite simple groups Number 3 Part I, Chapter A: Almost simple K-groups Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| title_short | The classification of the finite simple groups |
| title_sort | the classification of the finite simple groups part i chapter a almost simple k groups |
| topic | Groupes simples finis ram Finite simple groups |
| topic_facet | Groupes simples finis Finite simple groups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010176946&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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