Cohomology rings of finite groups: with an appendix: Calculations of cohomology rings of groups of order dividing 64
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2003
|
| Series: | Algebras and applications
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 761-771) and index |
| Physical Description: | XV, 776 S. |
| ISBN: | 1402015259 |
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MARC
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| 245 | 1 | 0 | |a Cohomology rings of finite groups |b with an appendix: Calculations of cohomology rings of groups of order dividing 64 |c by Jon F. Carlson, ... |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer Acad. Publ. |c 2003 | |
| 300 | |a XV, 776 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algebras and applications |v 3 | |
| 500 | |a Includes bibliographical references (p. 761-771) and index | ||
| 650 | 4 | |a Anneaux (Algèbre) | |
| 650 | 7 | |a Cohomologie |2 gtt | |
| 650 | 4 | |a Groupes finis | |
| 650 | 4 | |a Homologie | |
| 650 | 4 | |a Finite groups | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Rings (Algebra) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
xi
Acknowledgments
xv
1.
HOMOLOGICAL ALGEBRA
1
1.
Introduction I
2.
Complexes and Sequences
3
3.
Projective and
Injectivo
Modules
6
4.
Resolutions
8
5.
Ext
10
6.
Tensor Products and Tor
17
2.
GROUP ALGEBRAS
23
1.
Introduction
23
2.
Duality and Tensor Products
25
3.
Induction and Restriction
28
4.
Radicals. Socles and Projective Modules
33
5.
Degree Shifting
35
6.
The Stable Category
37
7.
Group Cohomology and Change of Coefficients
44
3.
PROJECTIVE RESOLUTIONS
47
1.
Introduction
47
2.
Minimal Resolutions
48
3.
The Bar Resolution
50
4.
Applications to Low Dimensional Cohomology
52
5.
Restrictions. Inflations and Transfers
55
4.
COHOMOLOGY PRODUCTS
ül
1.
Introduction
(¡1
2.
Yoneda Splices and Compositions of Chain Maps
(il
3.
Products and Group Algebras
ül
4.
Restriction. Inflation and Transfer
71
vii
viii COHOMOLOGY
RINGS OF FINITE GROUPS
5.
Cohomology Ring Computations
72
6.
Shifted Subgroups and Restrictions
76
7.
Automorphisms and Cohomology
78
5.
SPECTRAL SEQUENCES
87
1.
Introductions
87
2.
The Spectral Sequence of a Bicomplcx
88
3.
Products
92
4.
The Lyndon-Hochschild-Serre Spectral Sequence
94
5.
Extension Classes
99
6.
Minimal Resolutions and Convergence
103
7.
Exact Couples and the
Bockstein
Spectral Sequence
104
6.
NORMS AND THE COHOMOLOGY OF
WREATH PRODUCTS 111
1.
Introduction 111
2.
Wreath Products
112
3.
The Norm Map
115
4.
Examples and Applications
120
5.
Finite Generation of Cohomology
123
7.
STEENROD OPERATIONS
129
1.
Introduction
129
2.
The Steenrod Algebra and Modules
130
3.
The Steenrod Operations on Cohomology
134
4.
Cohomology and Modules Over the Steenrod Algebra
141
5.
The Cohomology of
Extraspecial 2-Groups 143
6.
The Cohomology of
Extraspecial
p-Groups
151
7.
Serre «
Theorem on the Vanishing of
Bocksteins 153
8.
VARIETIES AND ELEMENTARY ABELIAN SUBGROUPS
159
1.
Introduction
159
2.
Filtration« on Modules
160
3.
Vanishing Products of Cohomology Elements
169
4.
Minimal Primes in Cohomology Rings.
171
¡5.
The Stratification Theorem
174
9.
COHOMOLOGY RINGS OF MODULES
179
1.
Introduction
179
2.
Generalized Bocksteins Over Elementary Abelian Groups
181
3.
Rank Varieties and Cohomology Rings Over Elementary
Abelian Groups
186
4.
The Cohomological Support Variety of a Module
190
5.
Equating the Rank and Cohomological Support Varieties
192
G. The Tensor Product Theorem
198
Contenta
ix
7.
Properties of the Cohomological Support Varieties
202
10.
COMPLEXITY AND MULTIPLE COMPLEXES
209
1.
Introduction
209
2.
Notes on Dimension and Rates of Growth
210
3.
Complexity of Modules
214
4.
Varieties for Modules With Other Coefficient Rings
218
5.
Projective
Resolutions as Multiple Complexes
225
11.
DUALITY COMPLEXES
231
1.
Introduction
231
2.
Gaps in Cohoinology
231
3.
Poiiicaré
Duality Complexes
237
4.
Differentials in the
HSS
242
5.
Cohen-Macaulay
Cohoinology
Rings
245
G. Further Considerations
250
12.
TRANSFERS. DEPTH AND DETECTION
255
1.
Introduction
255
2.
Notes on Depth and Associated Primes 25(i
3.
Depth and the /¿-Rank of the Center
259
4.
Varieties and Transfers
202
5.
Detection and Depth-Essential Cohoinology
207
0.
Special Cases
272
7.
Associated Primes in Cohoinology
270
8.
Unstable Modules
279
13.
SUBGROUP COMPLEXES
283
1.
Introduction
283
2.
Poset
s
of Subgroups and Cell Complexes
284
3.
Homotopy Equivalence s and Equivariance
287
4.
Complexes of Posets of Finite Groups
292
5.
The
Bouc
Complex
295
0.
Applications to Cohomology
290
7.
Decompositions of
Moduless
300
S.
Additional Remarks 3()<s
9.
Homology Decompositions
310
14.
COMPUTER CALCULATIONS
AND COMPLETION TESTS
313
1.
Introduction
313
2.
Tłu1
Visual Cohoinology Ring: Generators and Relations
314
3.
Resolutions. Maps and Homogeneous Parameters
31*
4.
Tests for Completion
321
5.
Two Special Cases
331
χ
COHOMOLOGY RIXGS
OF FINITE GROUPS
Appendices: CALCULATIONS OF THE COHOMOLOGY
RIXGS OF GROUPS OF ORDER DIVIDING
04
by Jon F. Carlson. Luis Valero-Elizondo and Muchong Zhang
337
INTRODUCTION
338
A NOTATION AND REFERENCES
339
В
GROUPS OF ORDER
8 347
С
GROUPS OF ORDER
16 349
D- GROUPS OF ORDER
32 357
E- GROUPS OF ORDER
64 397
F- TABLES OF KRULL DIMENSION AND DEPTH
755
G- TABLES OF
HILBERT/POINCARÉ
SERIES
757
REFERENCES
761
INDEX
773
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| id | DE-604.BV019810432 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:06:39Z |
| institution | BVB |
| isbn | 1402015259 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013135858 |
| oclc_num | 53099072 |
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| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR |
| physical | XV, 776 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Algebras and applications |
| series2 | Algebras and applications |
| spelling | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 by Jon F. Carlson, ... Dordrecht [u.a.] Kluwer Acad. Publ. 2003 XV, 776 S. txt rdacontent n rdamedia nc rdacarrier Algebras and applications 3 Includes bibliographical references (p. 761-771) and index Anneaux (Algèbre) Cohomologie gtt Groupes finis Homologie Finite groups Homology theory Rings (Algebra) Algebraischer Ring (DE-588)4141855-4 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Algebraischer Ring (DE-588)4141855-4 s Algebraische Topologie (DE-588)4120861-4 s DE-604 Carlson, Jon F. 1940- Sonstige (DE-588)133287629 oth Algebras and applications 3 (DE-604)BV035420975 3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013135858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 Algebras and applications Anneaux (Algèbre) Cohomologie gtt Groupes finis Homologie Finite groups Homology theory Rings (Algebra) Algebraischer Ring (DE-588)4141855-4 gnd Endliche Gruppe (DE-588)4014651-0 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4141855-4 (DE-588)4014651-0 (DE-588)4120861-4 |
| title | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 |
| title_auth | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 |
| title_exact_search | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 |
| title_full | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 by Jon F. Carlson, ... |
| title_fullStr | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 by Jon F. Carlson, ... |
| title_full_unstemmed | Cohomology rings of finite groups with an appendix: Calculations of cohomology rings of groups of order dividing 64 by Jon F. Carlson, ... |
| title_short | Cohomology rings of finite groups |
| title_sort | cohomology rings of finite groups with an appendix calculations of cohomology rings of groups of order dividing 64 |
| title_sub | with an appendix: Calculations of cohomology rings of groups of order dividing 64 |
| topic | Anneaux (Algèbre) Cohomologie gtt Groupes finis Homologie Finite groups Homology theory Rings (Algebra) Algebraischer Ring (DE-588)4141855-4 gnd Endliche Gruppe (DE-588)4014651-0 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Anneaux (Algèbre) Cohomologie Groupes finis Homologie Finite groups Homology theory Rings (Algebra) Algebraischer Ring Endliche Gruppe Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013135858&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420975 |
| work_keys_str_mv | AT carlsonjonf cohomologyringsoffinitegroupswithanappendixcalculationsofcohomologyringsofgroupsoforderdividing64 |