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We investigate the Galois group G_S(p) of the maximal p-extension unramifiedoutside a finite set S of primes of a number field in the (mixed) case, whenthere are primes dividing p inside and outside S. We show that the cohomologyof G_S(p) is "often" isomorphic to the etale cohomology of the scheme Spec(O_k  S), in particular, G_S(p) is of cohomological dimension 2 then. We deducethis from the results in our previous paper "Rings of integers of typeK(\pi,1)" (arXiv:0705.3372), which mainly dealt with the tame case.

On the K(\pi,1)-property for rings of integers in the mixed case