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- W1994179999 abstract "Let K be any field, G be a finite group. Let G act on the rational function field K(xg:g∈G) by K-automorphisms defined by h⋅xg=xhg for any g,h∈G. Denote by K(G)=K(xg:g∈G)G the fixed field. Noether's problem asks, under what situations, the fixed field K(G) will be rational (= purely transcendental) over K. TheoremLet G be a finite group of order 32 with exponent e. If charK=2 or K is any field containing a primitive eth root of unity, then K(G) is rational over K. Theorem Let G be a finite group of order 32 with exponent e. If charK=2 or K is any field containing a primitive eth root of unity, then K(G) is rational over K." @default.
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- W1994179999 date "2008-10-01" @default.
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- W1994179999 title "Noether's problem for groups of order 32" @default.
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- W1994179999 doi "https://doi.org/10.1016/j.jalgebra.2008.07.007" @default.
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