Noether's problem for dihedral 2-groups

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Title:	Noether's problem for dihedral 2-groups
Authors:	Chu, Huah;Hu, Shou-jen;Kang, Ming-chang
Contributors:	淡江大學數學學系
Keywords:	Rationality;Noether's problem;generic Galois extension;generic polynomials;dihedral groups
Date:	2004-01
Issue Date:	2010-01-28
Publisher:	Zurich: European Mathematical Society
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. Noethers 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.
Relation:	Commentarii Mathematici Helvetici 79(1), pp.147-159
DOI:	10.1007/s00014-003-0783-8
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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