3-transposition groups:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
124 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 260 S. graph. Darst. |
| ISBN: | 0521571960 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804125859864379392 |
|---|---|
| adam_text | Contents
Part I: Fischer s Theory page 1
Introduction 1
1. Preliminaries 6
1. Categories 6
2. Elementary group theory 8
3. Permutation representations 12
4. Linear representations 14
5. Coxeter systems 16
2. Commuting graphs of groups 21
6. Graphs 21
7. Locally conjugate subsets of groups 25
3. The structure of 3 transposition groups 30
8. Basic results on 3 transpositions 30
9. The generalized Fitting subgroup of a 3 transposition group 33
4. Classical groups generated by 3 transpositions 39
10. The classical groups 39
11. Classical groups generated by 3 transpositions 44
5. Fischer s Theorem 58
12. A uniqueness lemma 59
13. Primitive 3 transposition groups 65
14. The case O2((Dd)) £ Z((Dd)) 70
15. The case O2((Dd)) Z((Dd)) O3((Z)rf» 75
16. The Fischer groups 82
17. Epilogue: The proof of Fischer s Theorem 87
v
vi Contents
6. The geometry of 3 transposition groups 91
18. Fischer spaces 91
19. A result of M. Hall, Jr. 94
20. Beyond Fischer s Theorem 101
Part II: The existence and uniqueness of the Fischer groups 109
Introduction 109
7. Some group extensions 113
21. Some 2 cohomology 113
22. The Todd modules for the Mathieu groups 121
23. Central extensions, Schur multipliers, and 1/6(2) 126
8. Almost 3 transposition groups 137
24. Sufficient conditions to be a 3 transposition group 137
25. Some results on 3 transposition groups 140
9. Uniqueness systems and coverings of graphs 147
26. Coverings and simple connectivity of graphs 147
27. Uniqueness systems 152
10. l/4(3) as a subgroup of f/6(2) 157
28. The C/4 (3) lattice 157
29. The embedding of £/4(3)/Z3 in SU6(2) 167
11. The existence and uniqueness of the Fischer groups 173
30. A characterization of U(, (2) 173
31. The uniqueness of groups of type M(22) 177
32. The uniqueness of groups of type M(23) 181
33. The uniqueness of groups of type M(24) 183
34. Groups of type F24 185
35. The uniqueness of groups of type Aut(F24) 193
36. The uniqueness of groups of type F24 195
Part III: The local structure of the Fischer groups 199
Introduction 199
12. The 2 local structure of the Fischer groups 201
37. Involutions and their centralizers in the Fischer groups 201
Contents vii
13. Elements of order 3 in orthogonal groups over GF(3) 211
38. Orthogonal groups 211
14. Odd locals in Fischer groups 226
39. Subgroups of odd prime order in M(22) 226
40. Subgroups of odd prime order in M(23) 233
41. Subgroups of odd prime order in M(24) 239
15. Normalizers of subgroups of prime order in Fischer groups 250
References 253
List of symbols 255
Index 257
|
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV011349897 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:08:16Z |
| institution | BVB |
| isbn | 0521571960 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007626836 |
| oclc_num | 246327991 |
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| physical | VII, 260 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Aschbacher, Michael 1944- Verfasser (DE-588)142400955 aut 3-transposition groups Michael Aschbacher Three-transposition groups 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 VII, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 124 Endliche einfache Gruppe (DE-588)4123136-3 gnd rswk-swf Endliche einfache Gruppe (DE-588)4123136-3 s DE-604 Cambridge tracts in mathematics 124 (DE-604)BV000000001 124 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007626836&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aschbacher, Michael 1944- 3-transposition groups Cambridge tracts in mathematics Endliche einfache Gruppe (DE-588)4123136-3 gnd |
| subject_GND | (DE-588)4123136-3 |
| title | 3-transposition groups |
| title_alt | Three-transposition groups |
| title_auth | 3-transposition groups |
| title_exact_search | 3-transposition groups |
| title_full | 3-transposition groups Michael Aschbacher |
| title_fullStr | 3-transposition groups Michael Aschbacher |
| title_full_unstemmed | 3-transposition groups Michael Aschbacher |
| title_short | 3-transposition groups |
| title_sort | 3 transposition groups |
| topic | Endliche einfache Gruppe (DE-588)4123136-3 gnd |
| topic_facet | Endliche einfache Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007626836&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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