Galois Theory of p-Extensions

  • Helmut Koch

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Helmut Koch
    Pages 1-2
  3. Helmut Koch
    Pages 3-15
  4. Helmut Koch
    Pages 21-40
  5. Helmut Koch
    Pages 41-48
  6. Helmut Koch
    Pages 49-52
  7. Helmut Koch
    Pages 53-58
  8. Helmut Koch
    Pages 59-76
  9. Helmut Koch
    Pages 77-92
  10. Helmut Koch
    Pages 93-97
  11. Helmut Koch
    Pages 99-110
  12. Helmut Koch
    Pages 111-131
  13. Helmut Koch
    Pages 133-148
  14. Helmut Koch
    Pages 149-161
  15. Back Matter
    Pages 163-191

About this book


First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introducing the theory of pro-p groups and their cohomology, it discusses presentations of the Galois groups G S of maximal p-extensions of number fields that are unramified outside a given set S of primes. It computes generators and relations as well as the cohomological dimension of some G S, and gives applications to infinite class field towers.The book demonstrates that the cohomology of groups is very useful for studying Galois theory of number fields; at the same time, it offers a down to earth introduction to the cohomological method. In a "Postscript" Helmut Koch and Franz Lemmermeyer give a survey on the development of the field in the last 30 years. Also, a list of additional, recent references has been included.


Cohomology Prime algebra chomology of groups class field towers number theory pro-p groups

Authors and affiliations

  • Helmut Koch
    • 1
  1. 1.Institut für MathematikHumboldt-Universität BerlinBerlinGermany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-07817-0
  • Online ISBN 978-3-662-04967-9
  • Series Print ISSN 1439-7382
  • Buy this book on publisher's site