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Galois Theory of p-Extensions

  • Kartonierter Einband
  • 208 Seiten
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First published in German in 1970 and translated into Russian in 1973, this classic now becomes available in English. After introd... Weiterlesen
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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.

Helmut Koch's classic now becomes available in English

Competently translated by Franz Lemmermeyer

Introduces the theory of pro-p groups and their cohomology

Contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer

Contains additional recent references

1. Profinite Groups.- 2. Galois Theory of Infinite Algebraic Extensions.- 3. Cohomology of Profinite Groups.- 4. Free pro-p Groups.- 5. Cohomological Dimension.- 6. Presentation of pro-p Groups.- 7. Group Algebras of pro-p Groups.- 8. Results from Algebraic Number Theory.- 9. The Maximal p-Extension.- 10. Local Fields of Finite Type.- 11. Global Fields of Finite Type.- 12. On p-Class Groups and p-Class Field Towers.- 13. The Cohomological Dimension of GS.- References.- Notation.- Postscript.- Additional References.- Author Index.


Titel: Galois Theory of p-Extensions
EAN: 9783642078170
ISBN: 3642078176
Format: Kartonierter Einband
Herausgeber: Springer Berlin Heidelberg
Anzahl Seiten: 208
Gewicht: 324g
Größe: H235mm x B155mm x T11mm
Jahr: 2010
Auflage: Softcover reprint of hardcover 1st ed. 2002

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