2015年11月
Noether's problem for groups of order 243
JOURNAL OF ALGEBRA
- ,
- ,
- ,
- 巻
- 442
- 号
- 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
- ID情報
-
- DOI : 10.1016/j.jalgebra.2015.03.010
- ISSN : 0021-8693
- eISSN : 1090-266X
- Web of Science ID : WOS:000362146600013