Galois Theory of p-Extensions
By: by Helmut Koch
Series: Springer Monographs in Mathematics; Springer Monographs in Mathematics
Publisher: Springer Berlin Heidelberg
Published: 2002
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 191
ISBN-13: 9783642078170; 9783662049679
Subjects: Group theory; Mathematics; K-theory
Description: 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.
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Table of contents: title: Profinite Groups; title: Galois Theory of Infinite Algebraic Extensions; title: Cohomology of Profinite Groups; title: Free pro-p Groups; title: Cohomological Dimension; title: Presentation of pro-p Groups; title: Group Algebras of pro-p Groups; title: Results from Algebraic Number Theory; title: The Maximal p-Extension; title: Local Fields of Finite Type; title: Global Fields of Finite Type; title: On p-Class Groups and p-Class Field Towers; title: The Cohomological Dimension of Gs.