First published in German in 1970 and translated into Russian in 1973 thisclassic now becomes available in English. After introducing the theory of prop groups ... » 

First published in German in 1970 and translated into Russian in 1973 thisclassic now becomes available in English. After introducing the theory of prop groups and their cohomology it discusses presentations of the Galois groupsG S of maximal IpIextensions of number fields that are unramified outside agiven set S of primes. It computes generators and relations as well as thecohomological dimension of some G S and gives applications to infinite classfield towers.The book demonstrates that the cohomology of groups is very usefulfor studying Galois theory of number fields at the same time it offers a downto earth introduction to the cohomological method. In a quotPostscriptquotHelmut Koch and Franz Lemmermeyer give a survey on the development of the fieldin the last 30 years. Also a list of additional recent references has beenincluded. TOCProfinite Groups. Galois Theory of Infinite AlgebraicExtensions. Cohomology of Profinite Groups. Free prop Groups. CohomologicalDimension. Presentation of prop Groups. Group Algebras of prop Groups.Results from Algebraic Number Theory. The Maximal IpIExtension. LocalFields of Finite Type. Global Fields of Finite Type. On pClass Groups and pClass Field Towers. The Cohomological Dimension of Gs. «