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...

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...

In diesem Buch wird ein ziemlich junges Gebiet der algebraischen Zahlentheorie behandelt. Es geht um die algebraische Theorie der p-Erweiterungen, die sich in den letzten 25 Jahren entwickelte und jetzt einen Vollkommenheitsgrad erreicht hat, welcher eine systematische Darstellung im hochsten MaBe wiinschenswert erscheinen HiBt. Diese Richtung in der Arithmetik beschiiftigt sich mit der Theorie der endlichen Erweiterungen von Korpem arithmetischen Typs. Das sind die . )J-adischen Zahl korper, die Korper der formalen Potenzreihen mit endlichen Konstantenkorpem, die algebraischen Zahlkorper und...