Ebook: Galois Theory of p-Extensions

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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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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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:
Front Matter....Pages i-xiii
Introduction....Pages 1-2
Profinite Groups....Pages 3-15
Galois Theory of Infinite Algebraic Extensions....Pages 17-20
Cohomology of Profinite Groups....Pages 21-40
Free pro-p Groups....Pages 41-48
Cohomological Dimension....Pages 49-52
Presentation of pro-p Groups....Pages 53-58
Group Algebras of pro-p Groups....Pages 59-76
Results from Algebraic Number Theory....Pages 77-92
The Maximal p-Extension....Pages 93-97
Local Fields of Finite Type....Pages 99-110
Global Fields of Finite Type....Pages 111-131
On p-Class Groups and p-Class Field Towers....Pages 133-148
The Cohomological Dimension of Gs ....Pages 149-161
Back Matter....Pages 163-191

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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.
Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-2
Profinite Groups....Pages 3-15
Galois Theory of Infinite Algebraic Extensions....Pages 17-20
Cohomology of Profinite Groups....Pages 21-40
Free pro-p Groups....Pages 41-48
Cohomological Dimension....Pages 49-52
Presentation of pro-p Groups....Pages 53-58
Group Algebras of pro-p Groups....Pages 59-76
Results from Algebraic Number Theory....Pages 77-92
The Maximal p-Extension....Pages 93-97
Local Fields of Finite Type....Pages 99-110
Global Fields of Finite Type....Pages 111-131
On p-Class Groups and p-Class Field Towers....Pages 133-148
The Cohomological Dimension of Gs ....Pages 149-161
Back Matter....Pages 163-191
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