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

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)].

### MSC:

 11R32 Galois theory 11R34 Galois cohomology

Zbl 0715.11065
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