A group-theoretical property of the ramification filtration

Let $\Gamma(p)$ be the Galois group of the maximal $p$-extension of a complete discrete valuation field with a perfect residue field of characteristic $p>0$. If $v_0>-1$ and $\Gamma(p)^{(v_0)}$ is the ramification subgroup of $\Gamma(p)$ in the upper numbering, we prove that any closed non-open finitely generated subgroup of the quotient $\Gamma(p)/\Gamma(p)^{(v_0)}$ is a free pro-$p$-group. In particular, this quotient has no torsion and no non-trivial commuting elements.