Noether's problem for dihedral 2-groups
Journal
Commentarii Mathematici Helvetici
Journal Volume
79
Journal Issue
1
Pages
147-159
Date Issued
2004
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 h ∈ 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. We shall prove that K(G) is rational over K if G is the dihedral group (resp. quasi-dihedral group, modular group) of order 16. Our result will imply the existence of the generic Galois extension and the existence of the generic polynomial of the corresponding group.
Type
journal article