  We investigate the Galois group $G_S(p)$ of the maximal $p$-extension
unramified outside a finite $S$ of primes of a number field in the (tame) case,
when no prime dividing $p$ is in $S$. We show that the cohomology of $G_S(p)$
is 'often' isomorphic to the etale cohomology of the scheme $\Spec(\O_k \sm
S)$, in particular, $G_S(p)$ is of cohomological dimension~2 then.
