Galois groups of $p$-extensions of higher local fields

Suppose $K$ is a finite extension of the field of $p$-adic numbers containing a primitive $p$-th root of unity. Then the Galois group $G(p)$ of the maximal $p$-extension of $K$ has finitely many generators and one (Demushkin) relation of very special form. In the talk we will discuss the structure of the maximal quotient of $G(p)$ of period $p$ and nilpotent class $<p$ in the case of local fields $K$ of dimension $>1$.