Profinite groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1998
|
| Schriftenreihe: | London Mathematical Society monographs / New series
19 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | IX, 284 S. graph. Darst. |
| ISBN: | 0198500823 |
Internformat
MARC
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| 035 | |a (OCoLC)40658188 | ||
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| 100 | 1 | |a Wilson, John S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Profinite groups |c John S. Wilson |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1998 | |
| 300 | |a IX, 284 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society monographs / New series |v 19 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Exercice groupe |2 Jussieu | |
| 650 | 7 | |a Groupe Galois |2 Jussieu | |
| 650 | 7 | |a Groupe profini |2 Jussieu | |
| 650 | 7 | |a Groupes profinis |2 ram | |
| 650 | 7 | |a Théorème Sylow |2 Jussieu | |
| 650 | 4 | |a Profinite groups | |
| 650 | 0 | 7 | |a Proendliche Gruppe |0 (DE-588)4132444-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Proendliche Gruppe |0 (DE-588)4132444-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 810 | 2 | |a New series |t London Mathematical Society monographs |v 19 |w (DE-604)BV045355493 |9 19 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008379015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008379015 | ||
Datensatz im Suchindex
| _version_ | 1804126984765177856 |
|---|---|
| adam_text | Contents
Leitfaden
χ
Notational
and terminological conventions
xi
0 Topological
preliminaries
1
0.1 Topological
spaces
1
0.2 Products
of
topological
spaces
3
0.3
Topological groups
6
0.4
Exercises
9
0.5
Notes
10
1
Profinite
groups and completions
11
1.1
Inverse limits
11
1.2
Characterizations of profinite groups
17
1.3
Transversals, complements and semidirect products
20
1.4
Completions
24
1.5
Completions of the integers
26
1.6
Exercises
29
1.7
Notes
33
2
Sylow theory
34
2.1
Indices of subgroups and Lagrange s theorem
34
2.2
Sylow s theorems
35
2.3
Hall subgroups
37
2.4
Pronilpotent groups
39
2.5
The Frattini subgroup
41
2.6
Fixed-point-free automorphisms
42
2.7
Exercises
44
2.8
Notes
46
3
Galois theory
47
3.1
The Galois group of an infinite extension
47
3.2
The fundamental theorem of Galois theory
49
3.3
All profinite groups are Galois groups
50
3.4
Exercises
51
3.5
Notes
52
4
Finitely generated groups and countably based groups
53
4.1
Characterizations of countably based groups
53
viii Contents
4.2
Finitely generated groups and finite images
56
4.3
Finitely generated groups and subgroups of finite index
59
4.4
Wreath products
61
4.5
An embedding theorem for pro
-С
groups
63
4.6
Exercises
64
4.7
Notes
66
5
Free groups and
projective
groups
68
5.1
Free pro
-С
groups
68
5.2
C-projective groups
74
5.3
Subgroups of
projective
groups
77
5.4
Open subgroups
81
5.5
A freeness criterion
83
5.6
Exercises
90
5.7
Notes
93
6
Modules, extensions and duality
94
6.1
Topological,
profinite
and discrete modules
94
6.2
Extension theory
97
102
105
113
113
114
114
117
119
122
126
127
129
136
137
Profinite
groups of finite rank
138
8.1
Notation and elementary results
138
8.2
Soluble groups of finite rank
139
8.3
Abelian subgroups
142
8.4
Arbitrary groups of finite rank
145
8.5
Pro-p groups of finite rank
147
8.6
Filtered and graded rings and modules
150
8.7
Graded algebras for pro-p groups
154
8.8
Exercises
161
8.9
Notes
6.3
Direct limits
6.4
Pontryagin duality
6.5
Exercises
6.6
Notes
Modules for completed group algebras
7.1
Completed group algebras
7.2
Modules for profinite rings
7.3
Completed group algebras of free pro-p groups
7.4
Free and
projective
modules
7.5
Local rings
7.6
Topologically free modules
7.7
Tensor products
7.8
Exercises
7.9
Notes
Contents ix
10
11
12
Cohomology
of
profinite
groups
164
9.1
Definition of cohomology groups
164
9.2
Compatible pairs of maps
166
9.3
The long exact sequence
167
9.4
Coinduced modules
171
9.5
Summary, and a calculation
174
9.6
Dimension shifting
176
9.7
The cohomology of
a profinite
group and its finite images
177
9.8
Cohomology groups from resolutions
181
9.9
Exercises
188
9.10
Notes
190
Further cohomological methods
191
10.1
The Eckmann-Shapiro lemma
191
10.2
Restriction, inflation and conjugation
193
10.3
The five-term cohomology sequence
196
10.4
Cup products
200
10.5
Homology groups
207
10.6
Exercises
208
10.7
Notes
209
Groups of finite cohomological dimension
210
11.1
Definition of cohomological dimension
210
11.2
Projective
groups
213
11.3
Higher cohomological dimension
215
11.4
Groups of dimension
2
217
11.5
A lemma of
Serre
222
11.6
A theorem of
Lazard
227
11.7
Exercises
235
11.8
Notes
237
Finitely presented pro-p groups
238
12.1
Notation and elementary results
238
12.2
Open subgroups, extensions and max-n
244
12.3
Demushkin groups
249
12.4
Finitely presented metabelian groups
260
12.5
The Golod-Shafarevich inequality and soluble groups
264
12.6
Exercises
271
12.7
Notes
272
Bibliography
274
Index
281
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:26:08Z |
| institution | BVB |
| isbn | 0198500823 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008379015 |
| oclc_num | 40658188 |
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| owner | DE-739 DE-20 DE-29T DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-739 DE-20 DE-29T DE-355 DE-BY-UBR DE-11 |
| physical | IX, 284 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | London Mathematical Society monographs / New series |
| spelling | Wilson, John S. Verfasser aut Profinite groups John S. Wilson Oxford Clarendon Press 1998 IX, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society monographs / New series 19 Hier auch später erschienene, unveränderte Nachdrucke Exercice groupe Jussieu Groupe Galois Jussieu Groupe profini Jussieu Groupes profinis ram Théorème Sylow Jussieu Profinite groups Proendliche Gruppe (DE-588)4132444-4 gnd rswk-swf Proendliche Gruppe (DE-588)4132444-4 s DE-604 New series London Mathematical Society monographs 19 (DE-604)BV045355493 19 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008379015&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wilson, John S. Profinite groups Exercice groupe Jussieu Groupe Galois Jussieu Groupe profini Jussieu Groupes profinis ram Théorème Sylow Jussieu Profinite groups Proendliche Gruppe (DE-588)4132444-4 gnd |
| subject_GND | (DE-588)4132444-4 |
| title | Profinite groups |
| title_auth | Profinite groups |
| title_exact_search | Profinite groups |
| title_full | Profinite groups John S. Wilson |
| title_fullStr | Profinite groups John S. Wilson |
| title_full_unstemmed | Profinite groups John S. Wilson |
| title_short | Profinite groups |
| title_sort | profinite groups |
| topic | Exercice groupe Jussieu Groupe Galois Jussieu Groupe profini Jussieu Groupes profinis ram Théorème Sylow Jussieu Profinite groups Proendliche Gruppe (DE-588)4132444-4 gnd |
| topic_facet | Exercice groupe Groupe Galois Groupe profini Groupes profinis Théorème Sylow Profinite groups Proendliche Gruppe |
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