  Every subfield $\kk(\phi)$ of the field of rational functions
$\kk(x_1,...,x_n)$ is contained in a unique maximal subfield of the form
$\kk(\psi)$. The element $\psi$ is called generative for the element $\phi$. A
subfield of $\kk(x_1,...,x_n)$ is called saturated if it contains a generative
element of each its element. We study the saturation property for subfields of
invariants $\kk(x_1,...,x_n)^G$, where $G$ is a finite group of automorphisms
of the field $\kk(x_1,...,x_n)$.
