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    Title: Noether's problem for groups of order 32
    Authors: Chu, Huah;Hu, Shou-Jen;Kang, Ming-Chang;Prokhorov, Y. G.
    Contributors: 淡江大學數學學系
    Keywords: Noether's problem;Rationality problem;Small groups
    Date: 2008-10
    Issue Date: 2010-01-28 07:08:02 (UTC+8)
    Publisher: Maryland Heights: Academic Press
    Abstract: Let K be any field, G be a finite group. Let G act on the rational function field by K-automorphisms defined by h⋅xg=xhg for any g,h∈G. Denote by the fixed field. Noether's problem asks, under what situations, the fixed field K(G) will be rational (= purely transcendental) over K.

    Theorem
    . Let G be a finite group of order 32 with exponent e. IfcharK=2or K is any field containing a primitive eth root of unity, thenK(G)is rational over K.
    Relation: Journal of Algebra 320(7), pp.3022-3035
    DOI: 10.1016/j.jalgebra.2008.07.007
    Appears in Collections:[數學學系暨研究所] 期刊論文

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