Noether's problem for four- and five-dimensional linear actions

JOURNAL OF ALGEBRA

卷:324

Article

Kitayama, Hidetaka

关键词: Noether's problem;    Rationality problem;    Inverse Galois problem;    Generic polynomials;   

DOI  :  10.1016/j.jalgebra.2010.04.029

来源: Elsevier

【 摘 要 】

Let G be a finite group. K be a field and G -> GL(V) be a faithful representation where v is a finite-dimensional vector space over K. In this paper, we will consider the problem which asks whether the fixed field K(V)(G) is rational (i.e purely transcendental) over K. This is a variant of Noether's problem. We will show the complete results of this problem in the case where G is a 2-group. K = Q and dim V = 4 and 5 Our results imply the existence of a generic polynomial for the corresponding group. (C) 2010 Elsevier Inc All rights reserved.

【 授权许可】

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