Cohomological methods in group theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Dekker
1972
|
| Schriftenreihe: | Pure and applied mathematics
11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 241 S. |
| ISBN: | 0824710312 |
Internformat
MARC
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| 300 | |a VII, 241 S. | ||
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| 490 | 1 | |a Pure and applied mathematics |v 11 | |
| 650 | 4 | |a Algèbre homologique | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface jii
Chapter 1. ELEMENTS OF HOMOLOGICAL ALGEBRA 1
1. Modules 1
2. Tensor Products 3
3. Existence of Tensor Products 4
4. The Homomorphism/(g ,? 7
5. Tensor Product of Algebras 9
6. Trilinear Maps 11
7. Exactness 12
8. Homology and Cohomology 18
9. Homotopy 23
10. Direct and Inverse Systems 25
Chapter 2. COHOMOLOGY OF FINITE GROUPS 32
11. Group Rings 32
12. The Trace Map 34
v
vi Contents
13. G Induced Modules 37
14. Complete Resolutions 38
15. The Dependence of H (G,M) on the G Module M 41
16. Existence of Complete Resolutions 46
17. The Uniqueness of Cohomology Groups 51
Chapter 3. COMPUTATIONS 55
18. The Computation of H~ KG, M) 55
19. The Standard Complete Resolution 57
20. Extensions 61
21. The Negative Cochain Complex 68
22. Homology and Cohomology of Monoids 74
23. Cohomology of Cyclic Groups 79
24. Trivial Action 84
Chapter 4. LOWER CENTRAL SERIES AND DIMENSION
SUBGROUPS 87
25. Dimension Subgroups 87
26. The Additive Group of Rationals mod 1 94
27. Polynomial Maps 96
28. Polynomial 2 Cocycles 99
29. Proof of D2(G) = G2 102
30. Remarks 105
Chapter 5. RELATIONS WITH SUBGROUPS AND
QUOTIENT GROUPS 107
31. Induced Homomorphisms 107
32. The Restriction and Corestriction (or Transfer) Maps 115
33. Sylow Subgroups 119
34. Generalization of G Induced Modules 120
35. The Inflation Map 122
36. Cohomological Triviality 127
37. Cohomological Equivalence 130
Chapter 6. FINITE p NILPOTENT GROUPS 135
38. Outer Automorphisms of Finite / Groups 135
39. Cohomological Characterization of Finite / Nilpotent Groups 139
40. Stable Elements 141
41. Frobenius Groups 143
Contents vjj
Chapter 7. CUP PRODUCTS 147
42. Definition of Cup Product 147
43. Properties of Cup Products 151
44. Uniqueness 152
45. Further Properties of Cup Products 155
46. Pairings 156
47. Duality 158
48. Periodicity 163
Chapter 8. SPECTRAL SEQUENCES 167
49. Differential Groups 167
50. How Spectral Sequences Are Used 175
51. The Cartan Leray Spectral Sequence 178
52. The Spectral Sequence of a Group Extension 181
53. The Hochschild Serre Spectral Sequence 183
54. Exact Sequences Involving the Terms of Spectral Sequences 189
55. A Decomposition of H (G, A) by Means of a Normal Hall Subgroup
of G 190
56. The Five Term Exact Sequence of Hochschild and Serre 192
57. Homology Spectral Sequences 194
Chapter 9. DESCENDING CENTRAL SERIES 196
58. A Homological Condition for Isomorphism of Nilpotent Groups 196
59. Existence of a Normal p Complement 199
60. A Condition for the Existence of Free Subgroups 201
61. Presentations and Free Subgroups 203
62. The Schur Multiplicator 206
Chapter 10. GALOIS GROUPS 214
63. Galois Groups 214
64. Abelian Galois Groups 222
65. Class Formations 227
BIBLIOGRAPHY 231
Indexes 237
|
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| id | DE-604.BV002624614 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:47:34Z |
| institution | BVB |
| isbn | 0824710312 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001686627 |
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| physical | VII, 241 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Babakhanian, Ararat Verfasser aut Cohomological methods in group theory Ararat Babakhanian New York Dekker 1972 VII, 241 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 11 Algèbre homologique Algèbre homologique ram Groupes, Théorie des ram Théorie des groupes Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Kohomologie (DE-588)4031700-6 s Gruppentheorie (DE-588)4072157-7 s DE-604 Pure and applied mathematics 11 (DE-604)BV000001885 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686627&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Babakhanian, Ararat Cohomological methods in group theory Pure and applied mathematics Algèbre homologique Algèbre homologique ram Groupes, Théorie des ram Théorie des groupes Gruppentheorie (DE-588)4072157-7 gnd Kohomologie (DE-588)4031700-6 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4031700-6 |
| title | Cohomological methods in group theory |
| title_auth | Cohomological methods in group theory |
| title_exact_search | Cohomological methods in group theory |
| title_full | Cohomological methods in group theory Ararat Babakhanian |
| title_fullStr | Cohomological methods in group theory Ararat Babakhanian |
| title_full_unstemmed | Cohomological methods in group theory Ararat Babakhanian |
| title_short | Cohomological methods in group theory |
| title_sort | cohomological methods in group theory |
| topic | Algèbre homologique Algèbre homologique ram Groupes, Théorie des ram Théorie des groupes Gruppentheorie (DE-588)4072157-7 gnd Kohomologie (DE-588)4031700-6 gnd |
| topic_facet | Algèbre homologique Groupes, Théorie des Théorie des groupes Gruppentheorie Kohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001686627&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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