RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 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

Full text: PDF file (402 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 512.623.22

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
\Bibitem{ArzPet09} \by I.~V.~Arzhantsev, A.~P.~Petravchuk \paper On the Saturation of Subfields of Invariants of Finite Groups \jour Mat. Zametki \yr 2009 \vol 86 \issue 5 \pages 659--663 \mathnet{http://mi.mathnet.ru/mz6354} \crossref{https://doi.org/10.4213/mzm6354} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2641338} \zmath{https://zbmath.org/?q=an:1188.13003} \transl \jour Math. Notes \yr 2009 \vol 86 \issue 5 \pages 625--628 \crossref{https://doi.org/10.1134/S0001434609110030} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000273362000003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-73949091107}