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The main theme of this thesis is the existence and properties of Galois extensions of algebraic number fields with Galois group isomorphic to the additive group of padic integers, in short procyclic extensions. However, extensions with nonabelian propgroups as Galois groups are also considered. The connection between procyclic extensions and Leopoldt's Conjecture is discussed. The notion of prationality is defined, and the classification of 2rational imaginary quadratic fields is given, apparently for the first time (correctly).
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