Profinite Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge: A Series of Modern Surveys in Mathematics
40 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. In neither of these two aspects have we tried to be encyclopedic. After some necessary background, we thoroughly develop the basic properties of profinite groups and introduce the main tools of the subject in algebra, topology and homol ogy. Later we concentrate on some topics that we present in detail, including recent developments in those areas. Interest in profinite groups arose first in the study of the Galois groups of infinite Galois extensions of fields. Indeed, profinite groups are precisely Galois groups and many of the applications of profinite groups are related to number theory. Galois groups carry with them a natural topology, the Krull topology. Under this topology they are Hausdorff compact and totally dis connected topological groups; these properties characterize profinite groups. Another important fact about profinite groups is that they are determined by their finite images under continuous homomorphisms: a profinite group is the inverse limit of its finite images. This explains the connection with abstract groups. If G is an infinite abstract group, one is interested in deducing prop erties of G from corresponding properties of its finite homomorphic images |
| Beschreibung: | 1 Online-Ressource (XIV, 435 p) |
| ISBN: | 9783662040973 9783642086328 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-662-04097-3 |
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Datensatz im Suchindex
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| author | Ribes, Luis |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-04097-3 |
| format | Electronic eBook |
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| id | DE-604.BV042423292 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662040973 9783642086328 |
| issn | 0071-1136 |
| language | English |
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| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge: A Series of Modern Surveys in Mathematics |
| spelling | Ribes, Luis Verfasser aut Profinite Groups by Luis Ribes, Pavel Zalesskii Berlin, Heidelberg Springer Berlin Heidelberg 2000 1 Online-Ressource (XIV, 435 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge: A Series of Modern Surveys in Mathematics 40 0071-1136 The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. In neither of these two aspects have we tried to be encyclopedic. After some necessary background, we thoroughly develop the basic properties of profinite groups and introduce the main tools of the subject in algebra, topology and homol ogy. Later we concentrate on some topics that we present in detail, including recent developments in those areas. Interest in profinite groups arose first in the study of the Galois groups of infinite Galois extensions of fields. Indeed, profinite groups are precisely Galois groups and many of the applications of profinite groups are related to number theory. Galois groups carry with them a natural topology, the Krull topology. Under this topology they are Hausdorff compact and totally dis connected topological groups; these properties characterize profinite groups. Another important fact about profinite groups is that they are determined by their finite images under continuous homomorphisms: a profinite group is the inverse limit of its finite images. This explains the connection with abstract groups. If G is an infinite abstract group, one is interested in deducing prop erties of G from corresponding properties of its finite homomorphic images Mathematics Group theory Topological Groups Number theory Topology Group Theory and Generalizations Topological Groups, Lie Groups Number Theory Mathematik Proendliche Gruppe (DE-588)4132444-4 gnd rswk-swf Proendliche Gruppe (DE-588)4132444-4 s 1\p DE-604 Zalesskii, Pavel Sonstige oth https://doi.org/10.1007/978-3-662-04097-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ribes, Luis Profinite Groups Mathematics Group theory Topological Groups Number theory Topology Group Theory and Generalizations Topological Groups, Lie Groups Number Theory Mathematik 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 by Luis Ribes, Pavel Zalesskii |
| title_fullStr | Profinite Groups by Luis Ribes, Pavel Zalesskii |
| title_full_unstemmed | Profinite Groups by Luis Ribes, Pavel Zalesskii |
| title_short | Profinite Groups |
| title_sort | profinite groups |
| topic | Mathematics Group theory Topological Groups Number theory Topology Group Theory and Generalizations Topological Groups, Lie Groups Number Theory Mathematik Proendliche Gruppe (DE-588)4132444-4 gnd |
| topic_facet | Mathematics Group theory Topological Groups Number theory Topology Group Theory and Generalizations Topological Groups, Lie Groups Number Theory Mathematik Proendliche Gruppe |
| url | https://doi.org/10.1007/978-3-662-04097-3 |
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