The local structure theorem for finite groups with a large p-subgroup:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
July 2016
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 242, number 1147 (4th of 4 numbers) |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029077806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | vii, 342 Seiten, 3 ungezählte Seiten |
| ISBN: | 9781470418779 |
Internformat
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| 245 | 1 | 0 | |a The local structure theorem for finite groups with a large p-subgroup |c U. Meierfrankenfeld, B. Stellmacher, G. Stroth |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c July 2016 | |
| 300 | |a vii, 342 Seiten, 3 ungezählte Seiten | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 242, number 1147 (4th of 4 numbers) | |
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| 700 | 1 | |a Stroth, Gernot |d 1949- |e Verfasser |0 (DE-588)1020107278 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1819316977971232768 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Definitions and Preliminary Results 15
1.1. Elementary Properties of Finite Groups 15
1.2. The Largest p-Reduced Elementary Abelian Normal Subgroup 22
. 1.3. pTrreducible Groups 26
1.4. T-Minimal Groups 29
1.5. Weakly Closed Subgroups 35
1.6. Large Subgroups 39
Chapter 2. The Case Subdivision and Preliminary Results 47
2.1. Notation and Elementary Properties 47
2.2. Asymmetry 50
2.3. Symmetric Pairs 59
2.4. Tall Natural Symplectic Modules 66
Chapter 3. The Orthogonal Groups 69
3.1. Notation and Elementary Properties 69
3.2. The Proof of Theorem C 75
Chapter 4. The Symmetric Case 93
4.1. The Proof of Theorem D 94
Chapter 5. The Short Asymmetric Case 113
Chapter 6. The Tall charp-Short Asymmetric Case 131
Chapter 7. The charp-Tall Q~Short Asymmetric Case 133
7.1. The Proof of Theorem G 134
Chapter 8. The Q-Tall Asymmetric Case I 159
8.1. Notation and Preliminary Results 160
8.2. The Case I ^ A 165
8.3. The Case 7^-4 and Q.XZ{A) ^ Z{L) 191
8.4. The Case 7 ^ A and SliZ(A) ^ Z{L) 191
8.5. The Proof of Theorem H 195
Chapter 9. The Q-tall Asymmetric Case II 197
9.1. Notation and Preliminary Results 198
9.2. The Proof of Theorem I 206
9.3. The Proof of Corollary 9.1 222
in
IV
Contents
9 4. The Proof of Corollary 9.2 224
Chapter 10. Proof of the Local Structure Theorem 229
10.1. Proof of Theorem J 230
10.2. Proof of the Local Structure Theorem 231
10.3. Proof of the Corollary to the Local Structure Theorem 239
Appendix A. Module theoretic Definitions and Results 241
A.l. Module-theoretic Definitions 241
A.2. Naming Modules 242
A.3. p-Reduced Modules 245
A.4. Wreath Product Modules 247
A. 5. Offenders 253
A.6. Nearly Quadratic Modules 258
A.7. Q ¡-Modules 259
A. 8. Genuine Groups of Lie Type 262
Appendix B. Classical Spaces and Classical Groups 267
B. l. Elementary Properties 269
B.2. The Classification of Classical Spaces 274
B.3. The Clifford Algebra 276
B.4. Normalizers of Singular Subspaces 280
B.5. Point-Stabilizers 281
B.6. Simplicity of the Natural Module 286
B.7. Normalizers of Classical Groups 288
B. 8. Q-Uniqueness in Classical Groups 291
Appendix C. FF-Module Theorems and Related Results 297
C. l. FF-Module Theorems 297
C.2. H1- and H2-Results 306
C. 3. Ql-Module Theorems 310
The Asymmetric Module Theorems 314
Appendix D. The Fitting Submodule 315
D. l. The Definition of the Fitting Submodule and Results from [MS2] 315
D.2. The Fitting Submodule and Large Subgroups 317
D. 3. The Nearly Quadratic Q -Module Theorem 317
Appendix E. The Amalgam Method 327
E. l. The Coset Graph 327
E.2. Elementary Properties 328
E.3. Critical Pairs 329
E.4. The Case I = 2 331
E.5. An Application of the Amalgam Method 333
Bibliography 335
Introduction 335
Sections 1-10 and Appendix 335
List of Symbols 339
Contents
v
List of Definitions
341
|
| any_adam_object | 1 |
| author | Meierfrankenfeld, Ulrich Stellmacher, Bernd 1944- Stroth, Gernot 1949- |
| author_GND | (DE-588)1012920070 (DE-588)1020107278 |
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV043664517 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:41:59Z |
| institution | BVB |
| isbn | 9781470418779 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029077806 |
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| physical | vii, 342 Seiten, 3 ungezählte Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spellingShingle | Meierfrankenfeld, Ulrich Stellmacher, Bernd 1944- Stroth, Gernot 1949- The local structure theorem for finite groups with a large p-subgroup Memoirs of the American Mathematical Society |
| title | The local structure theorem for finite groups with a large p-subgroup |
| title_auth | The local structure theorem for finite groups with a large p-subgroup |
| title_exact_search | The local structure theorem for finite groups with a large p-subgroup |
| title_full | The local structure theorem for finite groups with a large p-subgroup U. Meierfrankenfeld, B. Stellmacher, G. Stroth |
| title_fullStr | The local structure theorem for finite groups with a large p-subgroup U. Meierfrankenfeld, B. Stellmacher, G. Stroth |
| title_full_unstemmed | The local structure theorem for finite groups with a large p-subgroup U. Meierfrankenfeld, B. Stellmacher, G. Stroth |
| title_short | The local structure theorem for finite groups with a large p-subgroup |
| title_sort | the local structure theorem for finite groups with a large p subgroup |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029077806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT meierfrankenfeldulrich thelocalstructuretheoremforfinitegroupswithalargepsubgroup AT stellmacherbernd thelocalstructuretheoremforfinitegroupswithalargepsubgroup AT strothgernot thelocalstructuretheoremforfinitegroupswithalargepsubgroup |