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AuthorKoch, Helmut. author
TitleGalois Theory of p-Extensions [electronic resource] / by Helmut Koch
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
Connect tohttp://dx.doi.org/10.1007/978-3-662-04967-9
Descript XIII, 191 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Group theory K-theory Mathematics K-Theory Group Theory and Generalizations



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