Saturated subfields and invariants of finite groups

Abstract

Every subfield $\kk(ϕ)$ of the field of rational functions $\kk(x_1,...,x_n)$ is contained in a unique maximal subfield of the form $\kk(ψ)$. The element $\psi$ is called generative for the element $\varphi$. 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 $\kk(x_1,...,x_n)$.

4 pages, some remarks and new references are added

References in corpus (1)

• On closed rational functions in several variables