On the Saturation of Subfields of Invariants of Finite Groups

I. V. Arzhantsev ; A. P. Petravchuk

Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 659-663

Résumé

Every subfield $\mathbb K(\phi)$ of the field of rational fractions $\mathbb K(x_1,\dots,x_n)$ is contained in a unique maximal subfield of the form $\mathbb K(\psi)$. The element $\psi$ is said to be generating for the element $\phi$. A subfield of $\mathbb K(x_1,\dots,x_n)$ is said to be saturated if, together with every its element, the subfield also contains the generating element. In the paper, the saturation property is studied for the subfields of invariants $\mathbb K(x_1,\dots,x_n)^G$ of a finite group $G$ of automorphisms of the field $\mathbb K(x_1\dots,x_n)$.

Détail

Keywords: finite group, saturated subfield, polynomial ring, closed rational function, the groups $\operatorname{SL}_2(\mathbb C)$, $\operatorname{PSL}_2(\mathbb C)$.
Mots-clés : polynomial invariant, subalgebra of invariants