Noether's problem for dihedral 2-groups

  • Huah Chu

    National Taiwan University, Taipei, Taiwan
  • Shou-Jen Hu

    Tamkang University, Taipei, Taiwan
  • Ming-Chang Kang

    National Taiwan University, Taipei, Taiwan

Abstract

Let be any field and be a finite group. Let act on the rational function field by -automorphisms defined by for any . Denote by the fixed field . Noethers problem asks whether is rational (= purely transcendental) over . We shall prove that is rational over if 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.

Cite this article

Huah Chu, Shou-Jen Hu, Ming-Chang Kang, Noether's problem for dihedral 2-groups. Comment. Math. Helv. 79 (2004), no. 1, pp. 147–159

DOI 10.1007/S00014-003-0783-8