Noether's problem for dihedral 2-groups
Huah ChuNational Taiwan University, Taipei, Taiwan
Ming-Chang KangNational Taiwan University, Taipei, Taiwan
Shou-Jen HuTamkang University, Taipei, Taiwan
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, Ming-Chang Kang, Shou-Jen Hu, Noether's problem for dihedral 2-groups. Comment. Math. Helv. 79 (2004), no. 1, pp. 147–159DOI 10.1007/S00014-003-0783-8