淡江大學機構典藏:Item 987654321/41693
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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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