論文

査読有り 国際共著
2015年11月

Noether's problem for groups of order 243

JOURNAL OF ALGEBRA
  • Huah Chu
  • ,
  • Akinari Hoshi
  • ,
  • Shou-Jen Hu
  • ,
  • Ming-chang Kang

442
開始ページ
233
終了ページ
259
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.jalgebra.2015.03.010
出版者・発行元
ACADEMIC PRESS INC ELSEVIER SCIENCE

Let k be any field, G be a finite group. Let G act on the rational function field k(x(g) : g is an element of G) by k-automorphisms defined by h . x(g) = x(hg) for any g,h is an element of G. Denote by k(G) = k(x(g) : g is an element of G)(G) the fixed field. Noether's problem asks, under what situations, the fixed field k(G) will be rational (= purely transcendental) over k. According to the data base of GAP there are 10 isoclinism families for groups of order 243. It is known that there are precisely 3 groups G of order 243 (they consist of the isoclinism family Phi(10)) such that the unramified Brauer group of C(G) over C is non-trivial. Thus C(G) is not rational over C. We will prove that, if zeta(9) is an element of k, then k(G) is rational over k for groups of order 243 other than these 3 groups, except possibly for groups belonging to the isoclinism family Phi(7). (C) 2015 Elsevier Inc. All rights reserved.

リンク情報
DOI
https://doi.org/10.1016/j.jalgebra.2015.03.010
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000362146600013&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.jalgebra.2015.03.010
  • ISSN : 0021-8693
  • eISSN : 1090-266X
  • Web of Science ID : WOS:000362146600013

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