Advertisement

Profinite Groups

  • Luis Ribes
  • Pavel Zalesskii

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 40)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Luis Ribes, Pavel Zalesskii
    Pages 1-18
  3. Luis Ribes, Pavel Zalesskii
    Pages 19-77
  4. Luis Ribes, Pavel Zalesskii
    Pages 79-121
  5. Luis Ribes, Pavel Zalesskii
    Pages 123-163
  6. Luis Ribes, Pavel Zalesskii
    Pages 165-200
  7. Luis Ribes, Pavel Zalesskii
    Pages 201-257
  8. Luis Ribes, Pavel Zalesskii
    Pages 259-300
  9. Luis Ribes, Pavel Zalesskii
    Pages 301-360
  10. Luis Ribes, Pavel Zalesskii
    Pages 361-400
  11. Back Matter
    Pages 401-435

About this book

Introduction

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.

Keywords

Galois group Profinite group cohomology number theory topological group topology

Authors and affiliations

  • Luis Ribes
    • 1
  • Pavel Zalesskii
    • 2
  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.Department of MathematicsUniversity of BrasiliaBrasiliaBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-04097-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 2000
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08632-8
  • Online ISBN 978-3-662-04097-3
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site