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October, 2010 Some cases of four dimensional linear Noether's problem
J. Math. Soc. Japan 62(4): 1273-1288 (October, 2010). DOI: 10.2969/jmsj/06241273


The linear Noether's problem means the rationality problem for the fixed field of linear actions on the rational function field. This paper deals with a part of our study on the four dimensional linear Noether's problem. Apart from the main part of our study, which will be published in other papers, the results which require complicated calculations by a computer are published here as a separate paper. The problem is affirmative for all of 5 non-solvable subgroups and the largest and one of the second largest subgroups of GL(4,Q). As relevant topics, we remark that PSp(3,2) (the simple group of order 1451520) has a generic polynomial over Q.


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Aiichi YAMASAKI. "Some cases of four dimensional linear Noether's problem." J. Math. Soc. Japan 62 (4) 1273 - 1288, October, 2010.


Published: October, 2010
First available in Project Euclid: 2 November 2010

zbMATH: 1219.14019
MathSciNet: MR2761897
Digital Object Identifier: 10.2969/jmsj/06241273

Primary: 12F20
Secondary: 12F12

Keywords: finite reflection groups , generic polynomial , inverse Galois theorem , linear Noether's problem

Rights: Copyright © 2010 Mathematical Society of Japan

Vol.62 • No. 4 • October, 2010
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