Profinite groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Ausgabe: | 2. ed |
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
3. Folge ; 40 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [415] - 423 |
| Beschreibung: | XVI, 464 S. graph. Darst. |
| ISBN: | 9783642016417 9783642016424 |
Internformat
MARC
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| 245 | 1 | 0 | |a Profinite groups |c Luis Ribes ; Pavel Zalesskii |
| 250 | |a 2. ed | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XVI, 464 S. |b graph. Darst. | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |v 40 | |
| 500 | |a Literaturverz. S. [415] - 423 | ||
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| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020209392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents Preface to the Second Edition.....................................................................vii Preface to the First Edition.......................................................................... ix 1 Inverse and Direct Limits 1.1 1.2 1.3 2 Inverse or Projective Limits................................................................ Direct or Inductive Limits.................................................................. Note s. Comments and Further Reading.......................................... Profinite Groups 2.1 2.2 Pro-C Groups ........................................................................................ Basic Properties of Pro-C Groups................................................... Existence of Sections................................................................ Exactness of Inverse! Limits of Profinite Groups........... 2.3 The; Orelei՛ eif a Profinite Group anel Svlow Subgroups............. 2.4 Generators ............................................................................................... 2.5 Finitely Generate-el Profinite Groups.............................................. 2.6 Generators and Chains of Subgroups.............................................. 2.7 Pmcyclic Groups.................................................................................... 2.8 The Fruttini Subgroup of a Prafinite Group................................. 2.9 Pontryagin Duality for Profinite Groups........................................ 2.10 Pullbacks anel
Pushouts....................................................................... 2.11 Pmfinite Groups as Galois Groups................................................... 2.12 Neetes. Comments anel Further Reaeling.......................................... Analytic Pro-p Groups............................................................ Number of Generators of a Group anel of Its Profinite Completion.................................................................................. 3 1 14 18 19 28 29 31 32 42 44 47 51 52 58 66 68 72 73 74 Free Profinite Groups 3.1 3.2 3.3 Profinite! Topologies................................................................................ The Pro-C Completiem ....................................................................... The Completion Functor....................................................... Free Pro-C Groups............................................................................... Free Pro-C Group on a Set Converging to 1.................. 75 78 81 85 88
Table of Contents XIV 3.4 Maximal Pro-C Quotient Groups..................................................... 3.5 3.6 3.7 Characterization of Free Pro-C Groups ........................................ 98 Open Subgroups of Free Pro-C Groups ...........................................113 Notes, Comments and Further Reading.............................................11G A Problem of Grothendieck on Completions ..................117 9G 4 Some Special Profinite Groups 1.1 Powers of Elements with Exponents from Z.................................... 119 4.2 Subgroups of Finite՝ Index in a Profinite Group............................. 120 4.3 Prohnité Abelian Groups..................................................................... 129 4.4 Automorphism Group of a Prohnité Group.................................... 132 4.5 Automorphism Group of a Free Pro-p Group..................................137 4.G Prohnité Frobeiiius Groups.................................................................. 142 4.7 Torsion in the Prohnité Completion of a Group ........................... 148 4.8 Notes. Comments and Further Reading............................................. 154 Prohnité Torsion Groups.......................................................... 15G Normal Automorphisms............................................................ 157 5 Discrete and Profinite Modules 5.1 Prohnité Rings and Modules.................................................................159 Duality Between Diseride and Prohnité Modules .........165 5.2 Free Prohnité
Modules............................................................................1GG 5.3 G-niodules and Complete Group Algebras...................................... 1G9 The Complete Group Algebra................................................. 170 5.4 Projective and Injective Modules........................................................ 172 5.5 Complete Tensor Products..................................................................... 177 5.6 Prohnité G-spaces.....................................................................................180 5.7 Free Prohnito [RGJ-inodules ...............................................................189 5.8 Diagonal Actions.................................................................................... 190 5.9 Notes, Comments and Further Reading.............................................193 The Magnus Algebra and Free Pro-p Groups..................193 6 Homology and Cohomology of Profinite Groups G.l Review of Homological Algebra........................................................... 195 Right and Left Derived Functors...........................................199 Bifunctors.......................................................................................200 The Ext Functors ....................................................................... 201 The Tor Functors ....................................................................... 202 G.2 Cohomology with Coefficients in DMod([f?GJ) ..........................203 Standard Resolutions.................................................................205 The
Inhomogeneous Bar Resolution.................... 20G G.3 Homology with Coefficients in PMod([/?Gj)................................ 208 G.4 Cohomology Groups with Coefficients in DMod(G) .................212 G.5 The Functorial Behavior of H (G.A) and Hn(G.A) .................214 The Inflation Alap....................................................................... 215
Table of Contents XV G.6 H (G.A) as Derived Functors on DMod(G) ..........................220 6.7 Special Mappings............................................................................ 224 The Restriction Map in Cohomology..............................224 The Corestriction Map in Cohomology..........................225 The Corestriction Map in Homology..............................229 The Restriction Map in Homology..................................229 6.8 Homology and Cohomology Groups in Low Dimensions...........231 H2(G.A) and Extensions of Profinite Groups..............233 6.9 Extensions of Profiuite Groups with Abelian Kernel................238 6.10 Induced and Coinduced Module s ................................................242 6.11 The՝ Ineluceel Moelule Indį (Z?) for lí Open ..............................247 6.12 Note s, Comments and Further Reading......................................249 7 Cohomological Dimension 7.1 7.2 7.3 7.4 Basic Properties ejf Dimensiem........................................................251 The՝ Lynelon-Hochschild-Serre Spectral Sequence........................256 Cohomole)gie:al Dimension etf Subgroups ......................................261 Cohennoleegical Dimension e)f Normal Subgroups anel Quotients................................................................................... 266 7.5 Groups G with cdp{G) 1 ............................................................268 7.6 Projective Profinite: Groups............................................................271 7.7 Free Pro-p Groups and Cohome)le)gical
Dimension......................275 7.8 Gene:rate)rs and Relateers for Pro-;; Groups..................................278 7.9 Cup Proelucts....................................................................................282 7.10 Note;s. Comments anel Further Reading........................................288 Pro-p Groups G with one՝ Defining Relator ..................290 Peňncaré Groups ..................................................................290 8 Normal Subgroups of Free Pro-C Groups 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11 Normal Subgroup Gene՝rate՝el by a Subset of a Basis..................294 The 5-rank....................................................................................... 296 Accessible Subgroups ......................................................................302 Accessible Subgroups 11 with up(F/H) rank(ŕ ).................... 306 Homogeneous Pro-C Groups..........................................................313 Normal Subgroups............................................................................326 Proper Open Subgroups of Normal Subgroups............................ 335 The՝ Congruence Kerned of SLz(Z)................................................340 Sufficient Conditiems for Freenetss..................................................341 Characteeristie· Subgroups of Fre՝e՝ Pro-C Groups........................348 Notes. Comments anel Further Reaeling........................................351
XVI 9 Table of Contents Free Constructions of Profinite Groups 9.1 Free Pro-C Products ..............................................................................353 9.2 Amalgamated Free Pro-C Products................................................... 307 9.3 Coliomological Characterizations of Amalgamated Products. . 371 9.4 Pro-C HNN-extensions........................................................................... 382 9.5 Notes, Comments and Further Reading.............................................388 Open Questions........................................................................................................ 393 Appendix A: Spectral Sequences Л.1 Spectral Sequences .................................................................................397 A.2 Positive Spectral Sequences................................................................. 399 The Base Terms......................................................................... 100 The Fiber Terms....................................................................... 100 A.3 Spectral Sequence of a Filtered Complex..................................... 102 A.4 Spectral Sequences of a Double Complex.......................................405 A.5 Notes, Comments and Further Reading............................................100 Appendix B: A Different Characterization of Free Profinite Groups B.l Free vs Projective Profinite Groups................................................ 107 B.2 Notes. Comments and Further Reading......................................... 108 Appendix C: Presentations of
Profinite Groups C.l Presentations.......................................................................................... 109 C.2 Relation Modules................................................................................... 112 C.3 Notes, Comments and Further՛ Reading......................................... 110 Appendix D: Wreath Products and Some Subgroup Theorems D.l Permutational Wreath Products.........................................................419 D.2 The Nielsen-Schreier Theorem for Free Pro-C Groups............ 123 D.3 The Kurosh Subgroup Theorem for Profinite Groups.............. 125 Kurosh Systems......................................................................... 128 D.4 Subgroups of Projective Groups........................................................ 432 D.5 Quasifree Profinite Groups....................................................................434 D.6 Notes, Comments and Further Reading......................................... 138 Bibliography...............................................................................................................439 Index of Symbols......................................................................................................151 Index of Authors......................................................................................................155 Index of Terms 159
|
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| dewey-full | 512.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.23 |
| dewey-search | 512.23 |
| dewey-sort | 3512.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed |
| format | Book |
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| id | DE-604.BV036127011 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:37:29Z |
| institution | BVB |
| isbn | 9783642016417 9783642016424 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020209392 |
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| physical | XVI, 464 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |
| spelling | Ribes, Luis Verfasser aut Profinite groups Luis Ribes ; Pavel Zalesskii 2. ed Berlin [u.a.] Springer 2010 XVI, 464 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge 40 Literaturverz. S. [415] - 423 Proendliche Gruppe (DE-588)4132444-4 gnd rswk-swf Proendliche Gruppe (DE-588)4132444-4 s DE-604 Zalesskii, Pavel Verfasser aut Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 40 (DE-604)BV000899194 40 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020209392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ribes, Luis Zalesskii, Pavel Profinite groups Ergebnisse der Mathematik und ihrer Grenzgebiete 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 Luis Ribes ; Pavel Zalesskii |
| title_fullStr | Profinite groups Luis Ribes ; Pavel Zalesskii |
| title_full_unstemmed | Profinite groups Luis Ribes ; Pavel Zalesskii |
| title_short | Profinite groups |
| title_sort | profinite groups |
| topic | Proendliche Gruppe (DE-588)4132444-4 gnd |
| topic_facet | Proendliche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020209392&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT ribesluis profinitegroups AT zalesskiipavel profinitegroups |