On Galois groups of p-closed algebraic number fields with restricted ramification. II. (English) Zbl 0728.11058

Wingberg, Kay

J. Reine Angew. Math. 416, 187-194 (1991).

Pursuing earlier work the author shows that the Galois group \(G_ S\) of the maximal p-extension \(k_ S(p)\) of an algebraic number field k which is unramified outside a finite set S of primes containing the archimedean places and the primes above p is a free pro-p product of duality groups. This had already been proved by the author under the assumption on k to contain the 2pth roots of unity [J. Reine Angew. Math. 400, 185-202 (1989; Zbl 0715.11065)].

Reviewer: J.Ritter (Augsburg)

MSC:

11R32	Galois theory
11R34	Galois cohomology

Keywords:

Galois group; maximal p-extension; free pro-p product of duality groups

Citations:

Zbl 0715.11065