The classification of the finite simple groups: Number 4 Part II, Chapters 1 - 4: Uniqueness theorems
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
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Providence, Rhode Island
American Mathematical Society
[1999]
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| Series: | Mathematical surveys and monographs
Volume 40,4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 341 Seiten |
| ISBN: | 082181379X 9780821813799 |
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MARC
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| 245 | 1 | 0 | |a The classification of the finite simple groups |n Number 4 |p Part II, Chapters 1 - 4: Uniqueness theorems |c Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1999] | |
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 40,4 | |
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Contents
Preface xiii
PART II, CHAPTERS 1 4: UNIQUENESS THEOREMS
Chapter 1. General Lemmas 1
1. Uniqueness Elements 1
2. Permutation Groups 3
3. Two Theorems on Doubly Transitive Groups 7
4. Miscellaneous Lemmas 12
Chapter 2. Strongly Embedded Subgroups and Related Conditions on
Involutions 19
1. Introduction and Statement of Results 19
2. The Subsidiary Theorems 25
3. The Basic Setup and Counting Arguments 27
4. Reduction to the Simple Case: Theorem 1 33
5. p Subgroups Fixing Two or More Points: Theorem 2 38
6. A Reduction: Corollary 3 42
7. Double Transitivity and Xap0* '¦ Theorem 4 44
8. Reductions for Theorem SE 50
9. Good Subgroups of V Exist 54
10. The Structures of V and D 58
11. Proof of Theorem 6 (and Theorem SE) 62
12. The Group L = (z,t, [O2 {D),t]) 65
13. The Unitary Case 72
14. The Suzuki Case 74
15. The Linear Case 79
16. The Structure of D and Cx(u) 82
17. The Proof of Theorem ZD 88
18. The Weak 2 Generated 2 Core 91
19. The J2 Case 95
20. Bender Groups as 2 Components 98
21. Theorem SU: The 2 Central Case 101
22. The Jj Case 103
23. The 2A9 Case 105
24. Theorem SA: Strongly Closed Abelian 2 Subgroups 109
25. Theorem SF: Terminal Bender Components 112
26. Theorem SF: Product Disconnection 119
27. Theorem A9 127
ix
x CONTENTS
Chapter 3. p Component Uniqueness Theorems 131
1. Introduction 131
2. Theorem PUi: The Subsidiary Results 137
3. Exceptional Triples and 3C Group Lemmas 138
4. M Exceptional Subgroups of G 142
5. Centralizers of Elements of Xp(K*) 147
6. The Proofs of Theorems 1 and 2 150
7. Theorem 3: The Nonsimple Case 153
8. Theorem 3: The Simple Case 163
9. Theorem 4: Preliminaries 165
10. Normalizers of p Subgroups of K 168
11. The Case ~K 0 SS(p) 171
12. The SS(p) case 172
13. Theorem 5: The M Exceptional Case 179
14. The Residual M Exceptional Cases 188
15. Completion of the Proof of Theorem PUi: The p Rank 1 Case 193
16. Reductions to Theorem PUi 194
17. Further Reductions: The Non Normal Case 201
18. Theorem PU2: The Setup 206
19. The Case r p: A Reduction 208
20. The Case r = 1: Conclusion 211
21. The Case r = p = 2: A Reduction 214
22. The Case r = p = 2,K^ L2(q) 216
23. Theorem PU3: The Simple Case 220
24. The Residual Simple Cases 223
25. The Nonsimple Case 224
26. Theorem PU4 226
27. Corollaries PU2 and PU4 227
28. Aschbacher's Reciprocity Theorem 228
29. Theorem PU5 232
Chapter 4. Properties of 3C Groups 237
1. Automorphisms 237
2. Schur Multipliers and Covering Groups 238
3. Bender Groups 245
4. Groups of Low 2 Rank 253
5. Groups of Low p Rank, p Odd 256
6. Centralizers of Elements of Prime Order 257
7. Sylow 2 Subgroups of Specified 3C Groups 268
8. Disconnected Groups 271
9. Strongly Closed Abelian Subgroups 276
10. Generation 283
11. Generation and Terminal Components 293
12. Preuniqueness Subgroups and Generation 302
13. 2 Constrained Groups 328
14. Miscellaneous Results 331
Background References 333
Expository References 334
CONTENTS xi
Errata for Number 3, Chapter 14: Almost Simple X Groups 335
Glossary 338
Index of Terminology 340 |
| any_adam_object | 1 |
| author | Gorenstein, Daniel 1923-1992 Lyons, Richard 1945- Solomon, Ronald 1948- |
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| isbn | 082181379X 9780821813799 |
| language | English |
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| physical | xv, 341 Seiten |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | American Mathematical Society |
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| spelling | Gorenstein, Daniel 1923-1992 Verfasser (DE-588)1077470711 aut The classification of the finite simple groups Number 4 Part II, Chapters 1 - 4: Uniqueness theorems Daniel Gorenstein ; Richard Lyons ; Ronald Solomon Providence, Rhode Island American Mathematical Society [1999] xv, 341 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 40,4 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 4 Erscheint auch als Online-Ausgabe 978-1-4704-1269-2 Mathematical surveys and monographs Volume 40,4 (DE-604)BV000018014 40,4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010176952&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 4 Part II, Chapters 1 - 4: Uniqueness theorems Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| title_fullStr | The classification of the finite simple groups Number 4 Part II, Chapters 1 - 4: Uniqueness theorems Daniel Gorenstein ; Richard Lyons ; Ronald Solomon |
| title_full_unstemmed | The classification of the finite simple groups Number 4 Part II, Chapters 1 - 4: Uniqueness theorems 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 ii chapters 1 4 uniqueness theorems |
| 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=010176952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010647435 (DE-604)BV000018014 |
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