Saturated subfields and invariants of finite groups

Details Saturated subfields and invariants of finite groups Saturated subfields and invariants of finite groups

2008-08-22

arxiv.org/abs/0808.3132v3

Mat. Zametki 86:5 (2009), 659--663; transl. in Math. Notes 86 (2009), no. 5, 625--628

Mathematics

Rings and Algebras

4 pages, some remarks and new references are added

Scientific paper

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 $\kk(x_1,...,x_n)$.

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