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Denis Vogel

On the Galois group of 2-extensions with restricted rami?cation

In this paper we study the relation structure of the Galois group of the maximal outside a given set S of primes unramified 2-extension ?_S(2) of ? and of the Galois group of the 2-class field tower of a quadratic number field. We complete Morishita’s calculations of the triple Milnor invariants for ?_S(2) and obtain the relation structure of G(?_S(2) / ?) modulo the fourth step of the Zassenhaus filtration. We use this result in order to deduce information on the Galois group of the 2-class field tower of a quadratic number field.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 04/2005
Pages: 117 - 150

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