  We prove the non-degeneracy of the extremals of the Sobolev inequality
$$\int\limits_{\mathbb R^N}|\nabla u|^pdx\ge \mathcal S_p\int\limits_{\mathbb
R^N}|u|^{Np\over N-p}dx,\ u\in \mathcal D^{1,p}(\mathbb R^N)$$ when $1<p<N,$ as
solutions of a critical quasilinear equation involving the $p-$Laplacian.
