Corollary

If $n$ is invertible in $A$, $h_n$ is an isomorphism of the analytic manifold $G$ onto itself. For every non-zero ideal $a$ of $A$ contained in $m$, $h_n(G(a)) = G(a)$. For all $x \in G$, $\omega(x^n) = \omega(x)$.

This follows immediately from Proposition 8.