Journal of the Mathematical Society of Japan

Some cases of four dimensional linear Noether's problem

Aiichi YAMASAKI

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Abstract

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.

Article information

Source
J. Math. Soc. Japan Volume 62, Number 4 (2010), 1273-1288.

Dates
First available in Project Euclid: 2 November 2010

Permanent link to this document
http://projecteuclid.org/euclid.jmsj/1288703105

Digital Object Identifier
doi:10.2969/jmsj/06241273

Zentralblatt MATH identifier
05835143

Mathematical Reviews number (MathSciNet)
MR2761897

Subjects
Primary: 12F20: Transcendental extensions
Secondary: 12F12: Inverse Galois theory

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

Citation

YAMASAKI, Aiichi. Some cases of four dimensional linear Noether's problem. Journal of the Mathematical Society of Japan 62 (2010), no. 4, 1273--1288. doi:10.2969/jmsj/06241273. http://projecteuclid.org/euclid.jmsj/1288703105.


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