Abelian subgroups of Galois groups

The author proves that every Abelian subgroup of rank $>1$ in the Galois group $G=\operatorname{Gal}(\overline K/K)$ of the algebraic closure of a rational function field $K$ is contained in a ramification subgroup, and also that the unramified Brauer group $\operatorname{Br}_vK$ equals the unramified Brauer group $\operatorname{Br}_v(G^c)$ defined in [2], §3, where $G^c$ is the quotient group $ G^c= G/[[G,G],G]$.