02384nmm a2200313 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001700139245007500156260006300231300003300294505055600327653001600883653001700899653001300916653001600929653001300945653003700958710003400995041001901029989003801048490003901086856007401125082001101199520086001210EB000686919EBX0100000000000000054000100000000000000.0cr|||||||||||||||||||||140122 ||| eng a97836620496791 aKoch, Helmut00aGalois Theory of p-ExtensionshElektronische Ressourcecby Helmut Koch aBerlin, HeidelbergbSpringer Berlin Heidelbergc2002, 2002 aXIII, 191 pbonline resource0 a1. 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 aMathematics aGroup theory aK-theory aMathematics aK-Theory aGroup Theory and Generalizations2 aSpringerLink (Online service)07aeng2ISO 639-2 bSBAaSpringer Book Archives -20040 aSpringer Monographs in Mathematics uhttp://dx.doi.org/10.1007/978-3-662-04967-9?nosfx=yxVerlag3Volltext0 a512.66 aFirst 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