Geodesic
On the Saturation of Subfields of Invariants of Finite Groups
Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 659-663.

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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 $\mathbb K(x_1\dots,x_n)$.
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 
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I. V. Arzhantsev; A. P. Petravchuk. On the Saturation of Subfields of Invariants of Finite Groups. Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 659-663. http://geodesic.mathdoc.fr/item/MZM_2009_86_5_a1/

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