Noether's problem for metacyclic p-groups
Journal
Advances in Mathematics
Journal Volume
203
Journal Issue
2
Pages
554-567
Date Issued
2006
Author(s)
Abstract
Let K be any field and G be a finite group. Let G act on the rational function field K ( xg : g ∈ G ) by K-automorphisms defined by g · xh = xgh for any g, h ∈ G. Denote by K ( G ) the fixed field K ( xg : g ∈ G )G. Noether's problem asks whether K ( G ) is rational ( = purely transcendental) over K. An affirmative answer to Noether's problem for metacyclic p-groups will be proved provided that K contains enough roots of unity. © 2005 Elsevier Inc. All rights reserved.
Type
journal article