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Mat. Zametki, 2009, Volume 86, Issue 5, Pages 659–663 (Mi mz6354)  

On the Saturation of Subfields of Invariants of Finite Groups

I. V. Arzhantseva, A. P. Petravchukb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b National Taras Shevchenko University of Kyiv

Abstract: Every subfield $\mathbb K(\phi)$ of the field of rational fractions $\mathbb K(x_1,…,x_n)$ 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 $\mathbb K(x_1,…,x_n)$ 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 $\mathbb K(x_1,…,x_n)^G$ of a finite group $G$ of automorphisms of the field $\mathbb K(x_1…,x_n)$.

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

DOI: https://doi.org/10.4213/mzm6354

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English version:
Mathematical Notes, 2009, 86:5, 625–628

Bibliographic databases:

UDC: 512.623.22
Received: 24.07.2008

Citation: I. V. Arzhantsev, A. P. Petravchuk, “On the Saturation of Subfields of Invariants of Finite Groups”, Mat. Zametki, 86:5 (2009), 659–663; Math. Notes, 86:5 (2009), 625–628

Citation in format AMSBIB
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