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Bibliographic Details
Main Authors:	Ribes, Luis (Author), Zalesskij, Pavel (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2000
Series:	Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 40
Subjects:	Groepentheorie Groupes profinis Groupes, Théorie des Grupos profinitos Álgebra Profinite groups Proendliche Gruppe
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. [415] - 423
Physical Description:	XIV, 435 S. graph. Darst.
ISBN:	3540669868

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Record in the Search Index

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adam_text	TABLE OF CONTENTS PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII 1 INVERSE AND DIRECT LIMITS 1.1 INVERSE OR PROJECTIVE LIMITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 DIRECT OR INDUCTIVE LIMITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.3 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 18 2 PROFLNITE GROUPS 2.1 PRO - C GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 BASIC PROPERTIES OF PRO - C GROUPS . . . . . . . . . . . . . . . . . . . . . . 28 EXISTENCE OF SECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 EXACTNESS OF INVERSE LIMITS OF PROFLNITE GROUPS . . . . . 31 2.3 THE ORDER OF A PROFLNITE GROUP AND SYLOW SUBGROUPS . . . . . 32 2.4 GENERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.5 FINITELY GENERATED PROFLNITE GROUPS . . . . . . . . . . . . . . . . . . . . 45 2.6 GENERATORS AND CHAINS OF SUBGROUPS . . . . . . . . . . . . . . . . . . . . 48 2.7 PROCYCLIC GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.8 THE FRATTINI SUBGROUP OF A PROFLNITE GROUP . . . . . . . . . . . . . . 54 2.9 PONTRYAGIN DUALITY FOR PROFLNITE GROUPS . . . . . . . . . . . . . . . . . 60 2.10 PULLBACKS AND PUSHOUTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.11 PROFLNITE GROUPS AS GALOIS GROUPS . . . . . . . . . . . . . . . . . . . . . . 70 2.12 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 75 3 FREE PROFLNITE GROUPS 3.1 PROFLNITE TOPOLOGIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.2 THE PRO - C COMPLETION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 THE COMPLETION FUNCTOR . . . . . . . . . . . . . . . . . . . . . . . . 85 3.3 FREE PRO - C GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 FREE PRO - C GROUP ON A SET CONVERGING TO 1 . . . . . . . 93 3.4 MAXIMAL PRO - C QUOTIENT GROUPS . . . . . . . . . . . . . . . . . . . . . . . 101 3.5 CHARACTERIZATION OF FREE PRO - C GROUPS . . . . . . . . . . . . . . . . . . 103 3.6 OPEN SUBGROUPS OF FREE PRO - C GROUPS . . . . . . . . . . . . . . . . . . 117 XII TABLE OF CONTENTS 3.7 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 120 4 SOME SPECIAL PROFLNITE GROUPS 4.1 POWERS OF ELEMENTS WITH EXPONENTS FROM B Z . . . . . . . . . . . . . . 123 4.2 SUBGROUPS OF FINITE INDEX IN A PROFLNITE GROUP . . . . . . . . . . . 124 4.3 PROFLNITE ABELIAN GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.4 AUTOMORPHISM GROUP OF A PROFLNITE GROUP . . . . . . . . . . . . . . 136 4.5 AUTOMORPHISM GROUP OF A FREE PRO- P GROUP . . . . . . . . . . . . . 143 4.6 PROFLNITE FROBENIUS GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 4.7 TORSION IN THE PROFLNITE COMPLETION OF A GROUP . . . . . . . . . . . 154 4.8 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 160 5 DISCRETE AND PROFLNITE MODULES 5.1 PROFLNITE RINGS AND MODULES . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 DUALITY BETWEEN DISCRETE AND PROFLNITE MODULES . . . . 171 5.2 FREE PROFLNITE MODULES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 5.3 G -MODULES AND COMPLETE GROUP ALGEBRAS . . . . . . . . . . . . . . . 175 THE COMPLETE GROUP ALGEBRA . . . . . . . . . . . . . . . . . . . . 177 5.4 PROJECTIVE AND INJECTIVE MODULES . . . . . . . . . . . . . . . . . . . . . . . 179 5.5 COMPLETE TENSOR PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 5.6 PROFLNITE G -SPACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 5.7 FREE PROFLNITE [[ RG ]]-MODULES . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 5.8 DIAGONAL ACTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 5.9 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 199 6 HOMOLOGY AND COHOMOLOGY OF PROFLNITE GROUPS 6.1 REVIEW OF HOMOLOGICAL ALGEBRA . . . . . . . . . . . . . . . . . . . . . . . . . 201 RIGHT AND LEFT DERIVED FUNCTORS . . . . . . . . . . . . . . . . . 205 BIFUNCTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 THE EXT FUNCTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 THE TOR FUNCTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 6.2 COHOMOLOGY WITH COECIENTS IN DMOD ([[ RG ]]) . . . . . . . . . . . 210 STANDARD RESOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 6.3 HOMOLOGY WITH COECIENTS IN PMOD ([[ RG ]]) . . . . . . . . . . . . . 214 6.4 COHOMOLOGY GROUPS WITH COECIENTS IN DMOD ( G ) . . . . . . . 219 6.5 THE FUNCTORIAL BEHAVIOR OF H N ( G;A ) AND H N ( G;A ) . . . . . . . 220 THE INATION MAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 6.6 H N ( G;A ) AS DERIVED FUNCTORS ON DMOD ( G ) . . . . . . . . . . . . . 227 6.7 SPECIAL MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 THE RESTRICTION MAP IN COHOMOLOGY . . . . . . . . . . . . . . 231 THE CORESTRICTION MAP IN COHOMOLOGY . . . . . . . . . . . . 232 THE CORESTRICTION MAP IN HOMOLOGY . . . . . . . . . . . . . . 236 THE RESTRICTION MAP IN HOMOLOGY . . . . . . . . . . . . . . . . 236 6.8 HOMOLOGY AND COHOMOLOGY GROUPS IN LOW DIMENSIONS . . . . 238 TABLE OF CONTENTS XIII H 2 ( G;A ) AND EXTENSIONS OF PROFLNITE GROUPS . . . . . . 240 6.9 EXTENSIONS OF PROFLNITE GROUPS WITH ABELIAN KERNEL . . . . . . . 245 6.10 INDUCED AND COINDUCED MODULES . . . . . . . . . . . . . . . . . . . . . . . . 250 6.11 THE INDUCED MODULE IND G H ( B ) FOR H OPEN . . . . . . . . . . . . . . . 255 6.12 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 257 7 COHOMOLOGICAL DIMENSION 7.1 BASIC PROPERTIES OF DIMENSION . . . . . . . . . . . . . . . . . . . . . . . . . . 259 7.2 THE LYNDON-HOCHSCHILD-SERRE SPECTRAL SEQUENCE . . . . . . . . . . 264 7.3 COHOMOLOGICAL DIMENSION OF SUBGROUPS . . . . . . . . . . . . . . . . . . 269 7.4 COHOMOLOGICAL DIMENSION OF NORMAL SUBGROUPS AND QUOTIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 7.5 GROUPS G WITH CD P ( G ) * 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 7.6 PROJECTIVE PROFLNITE GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 7.7 FREE PRO- P GROUPS AND COHOMOLOGICAL DIMENSION . . . . . . . . . 284 7.8 GENERATORS AND RELATORS FOR PRO- P GROUPS . . . . . . . . . . . . . . . 287 7.9 CUP PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 7.10 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 298 8 NORMAL SUBGROUPS OF FREE PRO - C GROUPS 8.1 NORMAL SUBGROUP GENERATED BY A SUBSET OF A BASIS . . . . . . . 302 8.2 THE S -RANK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 8.3 ACCESSIBLE SUBGROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 8.4 ACCESSIBLE SUBGROUPS H WITH W 0 ( F=H ) RANK( F ) . . . . . . . . 315 8.5 HOMOGENEOUS PRO - C GROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 8.6 NORMAL SUBGROUPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 8.7 PROPER OPEN SUBGROUPS OF NORMAL SUBGROUPS . . . . . . . . . . . . 344 8.8 THE CONGRUENCE KERNEL OF SL 2 ( Z ) . . . . . . . . . . . . . . . . . . . . . . 349 8.9 SU*CIENT CONDITIONS FOR FREENESS . . . . . . . . . . . . . . . . . . . . . . . 350 8.10 CHARACTERISTIC SUBGROUPS OF FREE PRO - C GROUPS . . . . . . . . . . 357 8.11 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 360 9 FREE CONSTRUCTIONS OF PROFLNITE GROUPS 9.1 FREE PRO - C PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 9.2 AMALGAMATED FREE PRO - C PRODUCTS . . . . . . . . . . . . . . . . . . . . . 375 9.3 COHOMOLOGICAL CHARACTERIZATIONS OF AMALGAMATED PRODUCTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 9.4 PRO - C HNN-EXTENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 9.5 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 397 OPEN QUESTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 APPENDIX A1 SPECTRAL SEQUENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 XIV TABLE OF CONTENTS A2 POSITIVE SPECTRAL SEQUENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 A3 SPECTRAL SEQUENCE OF A FILTERED COMPLEX . . . . . . . . . . . . . . . . . 409 A4 SPECTRAL SEQUENCES OF A DOUBLE COMPLEX . . . . . . . . . . . . . . . . 411 A5 NOTES, COMMENTS AND FURTHER READING . . . . . . . . . . . . . . . . . . 413 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 INDEX OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 INDEX OF AUTHORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 INDEX OF TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
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series2	Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge
spelling	Ribes, Luis Verfasser (DE-588)114075100X aut Profinite groups Luis Ribes ; Pavel Zalesskii Berlin [u.a.] Springer 2000 XIV, 435 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge 40 Literaturverz. S. [415] - 423 Groepentheorie gtt Groupes profinis Groupes, Théorie des ram Grupos profinitos larpcal Álgebra larpcal Profinite groups Proendliche Gruppe (DE-588)4132444-4 gnd rswk-swf Proendliche Gruppe (DE-588)4132444-4 s DE-604 Zalesskij, Pavel Verfasser (DE-588)1067816542 aut Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 40 (DE-604)BV000899194 40 SWBplus Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008978890&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Ribes, Luis Zalesskij, Pavel Profinite groups Ergebnisse der Mathematik und ihrer Grenzgebiete Groepentheorie gtt Groupes profinis Groupes, Théorie des ram Grupos profinitos larpcal Álgebra larpcal 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 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	Groepentheorie gtt Groupes profinis Groupes, Théorie des ram Grupos profinitos larpcal Álgebra larpcal Profinite groups Proendliche Gruppe (DE-588)4132444-4 gnd
topic_facet	Groepentheorie Groupes profinis Groupes, Théorie des Grupos profinitos Álgebra Profinite groups Proendliche Gruppe
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008978890&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000899194
work_keys_str_mv	AT ribesluis profinitegroups AT zalesskijpavel profinitegroups

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