Reduction theorems for noether's problem
Resource
Proceedings of the American Mathematical Society 137 (6): 1867-1874
Journal
Proceedings of the American Mathematical Society
Journal Volume
137
Journal Issue
6
Pages
1867-1874
Date Issued
2009
Author(s)
Abstract
Let K be any field, and G be a finite group. Let G act on the rational function field K(x(g): g ∈ G)by K-automorphisms and h x(g) = x(hg). Denote by K(G) = K(x(g): g ∈ G)G the fixed field. Noether's problem asks whether K(G) is rational (= purely transcendental) over K. We will give several reduction theorems for solving Noether's problem. For example, let G̃ = G × H be a direct product of finite groups. Theorem. Assume that K(H) is rational over K.Then K(G̃)isrationalover K(G). In particular, if K(G) is rational (resp. retract rational) over K,sois K(G̃)over K. © 2009 American Mathematical Society.
Type
journal article
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