Symplectic amalgams:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong
Springer
2002
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 345 - 355 |
| Physical Description: | XI, 361 S. 24 cm |
| ISBN: | 1852334304 |
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MARC
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| 245 | 1 | 0 | |a Symplectic amalgams |c Christopher Parker ; Peter Rowley |
| 264 | 1 | |a London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong |b Springer |c 2002 | |
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| 490 | 0 | |a Springer monographs in mathematics | |
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Record in the Search Index
| _version_ | 1804129147097710592 |
|---|---|
| adam_text | Table of Contents
1 Introduction 1
1.1 Symplectic Amalgams 2
1.1.1 Notation 18
1.2 Goldchmidt G4 Amalgam Again 19
2 Preliminaries 21
2.1 Some Group Theory Results 22
2.2 Some Representation Theory Results 29
2.3 Sesquilinear Forms 35
2.4 Two Theorems of McLaughlin 40
2.5 Ultraspecial and Extraspecial Groups 42
2.6 Tensor Products and Group Actions on p Groups 45
2.7 The Goldschmidt Amalgams 48
3 The Structure of SL2(g) and its Modules 53
3.1 Group Theoretic Properties of SL2(g) 53
3.2 Modules for SL2(g) 56
4 Elementary Properties of Symplectic Amalgams 67
4.1 The Coset Graph 67
4.2 Proof of Theorem 1.6 69
5 The Structure of Qa 81
6 The L^ Chief Factors inV^ 93
7 Reduced Symplectic Amalgams 113
7.1 A Reduced Symplectic Subamalgam 113
7.2 Reduced Amalgams and Consequences of Theorem 6.1 118
8 The Largest Normal p Subgroup of Lp/Q0 125
9 The Components of Lp/Qp 141
9.1 The Action of Lp on Compp{L0) 142
9.2 Two or more Normal Components in Lp/Qp 148
ix
x Table of Contents
10 The Reduction to Quasisimple when CUa,(Ua/Za) £. Q0 .. 163
11 A First Look at the Amalgams with Vp/Z(y^) — q4 177
11.1 A Characteristic 3 Amalgam 178
11.2 The Proof of Theorem 11.1 180
12 The Story so Far 187
13 Groups of Lie Type 189
13.1 Weyl Groups and Parabolic Subgroups 193
13.2 Sylow p subgroups of Lie Type Groups 195
13.3 Automorphisms and Centres 197
13.4 The Order of Abelian p subgroups 199
13.5 Extremal Subgroups 202
14 Modules for Groups of Lie Type 215
14.1 Modules in Characteristic p 215
14.2 Module Results for Low Rank Groups of Lie Type 220
14.3 Modules for Lie Type Groups and (2, g) Transvections 224
14.4 Natural Modules for Orthogonal Groups , 231
14.5 Natural Modules for the Symplectic Groups 234
14.6 Natural Modules for G2(q) 237
14.7 Some Spin Modules 239
14.8 Modules for Lie Type Groups in Non defining Characteristic . 240
14.9 Some Non containments 247
15 Sporadic Simple Groups and Their Modules 249
16 Alternating Groups and Their Modules 257
17 Rank One Groups 265
18 Lie Type Groups in Characteristic p and Rank 2 271
18.1 A Subamalgam of .A 272
18.2 The Examples 285
18.3 L(s/Q0 a Symplectic Group and Vp/Z{Vp) a Spin Module ... 290
19 Lie Type Groups and Natural Modules 293
19.1 The Symplectic and Orthogonal Groups 295
19.2 Sp4(2) A Special Case 305
19.3 Groups of Type G2(q) 310
20 Lie Type Groups in Characteristic not p 313
Table of Contents xi
21 Alternating Groups 315
21.1 Large Alternating Groups 315
21.2 Small Alternating Groups 319
22 Sporadic Simple Groups 325
23 The Proof of the Main Theorems 327
24 A Brief Survey of Amalgam Results 331
24.1 Amalgam Results 331
24.2 Pushing up 340
References 345
Index 357
|
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| id | DE-604.BV014256748 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:00:31Z |
| institution | BVB |
| isbn | 1852334304 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009776792 |
| oclc_num | 48980054 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XI, 361 S. 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Parker, Christopher Verfasser aut Symplectic amalgams Christopher Parker ; Peter Rowley London ; Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong Springer 2002 XI, 361 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 345 - 355 Amalgams (Group theory) Symplectic groups Symplektische Gruppe (DE-588)4276585-7 gnd rswk-swf Amalgam Gruppentheorie (DE-588)4272864-2 gnd rswk-swf Symplektische Gruppe (DE-588)4276585-7 s Amalgam Gruppentheorie (DE-588)4272864-2 s DE-604 Rowley, Peter Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009776792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parker, Christopher Rowley, Peter Symplectic amalgams Amalgams (Group theory) Symplectic groups Symplektische Gruppe (DE-588)4276585-7 gnd Amalgam Gruppentheorie (DE-588)4272864-2 gnd |
| subject_GND | (DE-588)4276585-7 (DE-588)4272864-2 |
| title | Symplectic amalgams |
| title_auth | Symplectic amalgams |
| title_exact_search | Symplectic amalgams |
| title_full | Symplectic amalgams Christopher Parker ; Peter Rowley |
| title_fullStr | Symplectic amalgams Christopher Parker ; Peter Rowley |
| title_full_unstemmed | Symplectic amalgams Christopher Parker ; Peter Rowley |
| title_short | Symplectic amalgams |
| title_sort | symplectic amalgams |
| topic | Amalgams (Group theory) Symplectic groups Symplektische Gruppe (DE-588)4276585-7 gnd Amalgam Gruppentheorie (DE-588)4272864-2 gnd |
| topic_facet | Amalgams (Group theory) Symplectic groups Symplektische Gruppe Amalgam Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009776792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT parkerchristopher symplecticamalgams AT rowleypeter symplecticamalgams |