Noether's problem for groups of order 32

被引：27

作者：

Chu, Huah ^{[1
]}

Hu, Shou-Jen ^{[2
]}

Kang, Ming-chang ^{[1
,3
]}

Prokhorov, Y. G. ^{[4
]}

机构：

[1] Natl Taiwan Univ, Dept Math, Taipei 10764, Taiwan

[2] Tamkang Univ, Dept Math, Taipei, Taiwan

[3] Natl Taiwan Univ, Taida Inst Math Sci, Taipei 10764, Taiwan

[4] Moscow MV Lomonosov State Univ, Dept Algebra, Fac Math & Mech, Moscow, Russia

来源：

JOURNAL OF ALGEBRA | 2008年 / 320卷 / 07期

关键词：

Noether's problem; rationality problem; small groups;

D O I：

10.1016/j.jalgebra.2008.07.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let K be any field, G be a finite group. Let G act on the rational function field K(x(g): g is an element of G) by K-automorphisms defined by h . x(g) = x(hg) for any g, h is an element of G. Denote by K (G) = K(x(g): g is an element of G)(G) the fixed field. Noether's problem asks, under what situations, the fixed field K(G) will be rational (= purely transcendental) over K. Theorem. Let G be a finite group of order 32 with exponent e. If char K = 2 or K is any field containing a primitive eth root of unity, then K(G) is rational over K. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：3022 / 3035

页数：14