教師資料查詢 | 類別: 期刊論文 | 教師: 胡守仁 HU SHOU-JEN (瀏覽個人網頁)

標題:Noether's problem for dihedral 2-groups
學年92
學期1
出版(發表)日期2004/01/01
作品名稱Noether's problem for dihedral 2-groups
作品名稱(其他語言)
著者Chu, Huah; Hu, Shou-jen; Kang, Ming-chang
單位淡江大學數學學系
出版者Zurich: European Mathematical Society
著錄名稱、卷期、頁數Commentarii Mathematici Helvetici 79(1), pp.147-159
摘要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.
關鍵字Rationality; Noether's problem; generic Galois extension; generic polynomials; dihedral groups
語言英文
ISSN0010-2571;1420-8946
期刊性質國外
收錄於SCI
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