Lower central and dimension series of groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Lecture notes in mathematics
1952 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 346 S. |
| ISBN: | 9783540858171 9783540858188 |
Internformat
MARC
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| 100 | 1 | |a Michailov, Roman |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lower central and dimension series of groups |c Roman Mikhailov ; Inder Bir Singh Passi |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XXI, 346 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1952 | |
| 650 | 4 | |a Algèbre homologique | |
| 650 | 4 | |a Théorie des groupes | |
| 650 | 4 | |a Algebra, Homological | |
| 650 | 4 | |a Group theory | |
| 650 | 0 | 7 | |a Reihe |g Gruppentheorie |0 (DE-588)7635869-0 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Lecture notes in mathematics |v 1952 |w (DE-604)BV000676446 |9 1952 | |
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Datensatz im Suchindex
| _version_ | 1805078481148575744 |
|---|---|
| adam_text |
Contents
Lower
Central
Series
. 1
1.1
Commutator Calculus
. 1
1.2
Residually
Nilpotent
Groups
. 2
1.3
Generalized Relation Modules
. 17
1.4
k-central Extensions
. 37
1.5 Nilpotent
Completion
. 66
1.6
Bousfield-Kan Completion
. 71
1.7
Homological Localization
. 75
1.8
Crossed Modules and Cat^Groups
. 84
Dimension Subgroups
. 101
2.1
Groups Without Dimension Property
. 101
2.2 Sjögren's
Theorem
. 119
2.3
Fourth Dimension Subgroup
. 121
2.4
Fifth Dimension Subgroup
. 123
2.5
Quasi-varieties of Groups
. 134
2.6
The Quasi-variety V4
. 137
2.7
Dimension Quotients
. 143
2.8
Plotkin's Problems
. 148
2.9
Modular Dimension Subgroups
. 151
2.10
Lie Dimension Subgroups
. 152
2.11
Lie Nilpotency Indices
. 160
2.12
Subgroups Dual to Dimension Subgroups
. 163
Derived Series
. 165
3.1
Commutator Subgroups of Free
Nilpotent
Groups
. 165
3.2
E
and 17-groups
. 171
3.3
Transfinite
Derived Series
. 176
3.4
Applications to Asphericity
. 179
xviii Contents
4 Augmentation Powers.187
4.1 Augmentation
Identities
.187
4.2 Integral Augmentation Powers.187
4.3
Intersection
Theorems.190
4.4
Transfinite
Augmentation Powers.191
4.5 Schur
Multiplicator
.196
4.6 Relative Dimension
Subgroups
.210
4.7
A Characterization of Para-free Groups
.214
4.8
T-para-free Groups
.215
4.9
Homological Localization of Zjtrj-modules
.219
5
Homotopical Aspects
.229
5.1
The Associated Graded Ring of a Group Ring
.229
5.2
Spectral Sequences
.233
5.3
Applications to Dimension Subgroups
.243
5.4
Homotopical Applications
.254
5.5
Computations and Connectivity Results
.272
6
Miscellanea
.291
6.1
Power-closed Groups
.291
6.2
Braid Groups
.291
6.3
3-dimensional Surgery
.293
6.4
Vanishing Sums of Roots of Unity
.295
6.5
Fundamental Groups of
Projective
Curves
.296
A Simplicial Methods
.299
A.I Chain Complexes
.299
A.2 Simplicial Objects
.300
A.3 Geometric Realization Functor
.302
A.4 Skeleton and Coskeleton Functors
.302
A.5 Moore Complex and Homotopy Groups
.304
A.6 Dold-Kan Correspondence
.306
A.7 Eilenberg-Zilber Equivalence
.307
A.8 Classifying Functor
W
and Homology
.308
A.9 Bisimplicial Groups
.309
A.10 Certain Simplicial Constructions
.310
A.ll Free Simplicial Resolutions
.314
A.12 Functorial Properties
.317
A.13 Derived Functors
.320
A.
14
Quadratic Functors
.322
A.15 Derived Functors in the Sense of
Dold
and
Puppe .326
A.
16
Derived Limits and Fibration Sequence
.328
References
.331
Index
.343 |
| adam_txt |
Contents
Lower
Central
Series
. 1
1.1
Commutator Calculus
. 1
1.2
Residually
Nilpotent
Groups
. 2
1.3
Generalized Relation Modules
. 17
1.4
k-central Extensions
. 37
1.5 Nilpotent
Completion
. 66
1.6
Bousfield-Kan Completion
. 71
1.7
Homological Localization
. 75
1.8
Crossed Modules and Cat^Groups
. 84
Dimension Subgroups
. 101
2.1
Groups Without Dimension Property
. 101
2.2 Sjögren's
Theorem
. 119
2.3
Fourth Dimension Subgroup
. 121
2.4
Fifth Dimension Subgroup
. 123
2.5
Quasi-varieties of Groups
. 134
2.6
The Quasi-variety V4
. 137
2.7
Dimension Quotients
. 143
2.8
Plotkin's Problems
. 148
2.9
Modular Dimension Subgroups
. 151
2.10
Lie Dimension Subgroups
. 152
2.11
Lie Nilpotency Indices
. 160
2.12
Subgroups Dual to Dimension Subgroups
. 163
Derived Series
. 165
3.1
Commutator Subgroups of Free
Nilpotent
Groups
. 165
3.2
E
and 17-groups
. 171
3.3
Transfinite
Derived Series
. 176
3.4
Applications to Asphericity
. 179
xviii Contents
4 Augmentation Powers.187
4.1 Augmentation
Identities
.187
4.2 Integral Augmentation Powers.187
4.3
Intersection
Theorems.190
4.4
Transfinite
Augmentation Powers.191
4.5 Schur
Multiplicator
.196
4.6 Relative Dimension
Subgroups
.210
4.7
A Characterization of Para-free Groups
.214
4.8
T-para-free Groups
.215
4.9
Homological Localization of Zjtrj-modules
.219
5
Homotopical Aspects
.229
5.1
The Associated Graded Ring of a Group Ring
.229
5.2
Spectral Sequences
.233
5.3
Applications to Dimension Subgroups
.243
5.4
Homotopical Applications
.254
5.5
Computations and Connectivity Results
.272
6
Miscellanea
.291
6.1
Power-closed Groups
.291
6.2
Braid Groups
.291
6.3
3-dimensional Surgery
.293
6.4
Vanishing Sums of Roots of Unity
.295
6.5
Fundamental Groups of
Projective
Curves
.296
A Simplicial Methods
.299
A.I Chain Complexes
.299
A.2 Simplicial Objects
.300
A.3 Geometric Realization Functor
.302
A.4 Skeleton and Coskeleton Functors
.302
A.5 Moore Complex and Homotopy Groups
.304
A.6 Dold-Kan Correspondence
.306
A.7 Eilenberg-Zilber Equivalence
.307
A.8 Classifying Functor
W
and Homology
.308
A.9 Bisimplicial Groups
.309
A.10 Certain Simplicial Constructions
.310
A.ll Free Simplicial Resolutions
.314
A.12 Functorial Properties
.317
A.13 Derived Functors
.320
A.
14
Quadratic Functors
.322
A.15 Derived Functors in the Sense of
Dold
and
Puppe .326
A.
16
Derived Limits and Fibration Sequence
.328
References
.331
Index
.343 |
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| author | Michailov, Roman Passi, Inder Bir Singh 1939-2021 |
| author_GND | (DE-588)12104257X |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 200f |
| ctrlnum | (OCoLC)264693625 (DE-599)DNB989847624 |
| dewey-full | 510 512.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512.6 |
| dewey-search | 510 512.6 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV035139997 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:26:49Z |
| indexdate | 2024-07-20T06:29:45Z |
| institution | BVB |
| isbn | 9783540858171 9783540858188 |
| language | English |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Michailov, Roman Verfasser aut Lower central and dimension series of groups Roman Mikhailov ; Inder Bir Singh Passi Berlin [u.a.] Springer 2009 XXI, 346 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1952 Algèbre homologique Théorie des groupes Algebra, Homological Group theory Reihe Gruppentheorie (DE-588)7635869-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Reihe Gruppentheorie (DE-588)7635869-0 s DE-604 Gruppentheorie (DE-588)4072157-7 s b DE-604 Passi, Inder Bir Singh 1939-2021 Verfasser (DE-588)12104257X aut Lecture notes in mathematics 1952 (DE-604)BV000676446 1952 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Michailov, Roman Passi, Inder Bir Singh 1939-2021 Lower central and dimension series of groups Lecture notes in mathematics Algèbre homologique Théorie des groupes Algebra, Homological Group theory Reihe Gruppentheorie (DE-588)7635869-0 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)7635869-0 (DE-588)4072157-7 |
| title | Lower central and dimension series of groups |
| title_auth | Lower central and dimension series of groups |
| title_exact_search | Lower central and dimension series of groups |
| title_exact_search_txtP | Lower central and dimension series of groups |
| title_full | Lower central and dimension series of groups Roman Mikhailov ; Inder Bir Singh Passi |
| title_fullStr | Lower central and dimension series of groups Roman Mikhailov ; Inder Bir Singh Passi |
| title_full_unstemmed | Lower central and dimension series of groups Roman Mikhailov ; Inder Bir Singh Passi |
| title_short | Lower central and dimension series of groups |
| title_sort | lower central and dimension series of groups |
| topic | Algèbre homologique Théorie des groupes Algebra, Homological Group theory Reihe Gruppentheorie (DE-588)7635869-0 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Algèbre homologique Théorie des groupes Algebra, Homological Group theory Reihe Gruppentheorie Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016807402&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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