Rationality problem for some meta-abelian groups

JOURNAL OF ALGEBRA

卷:322

Article

Kang, Ming-chang^1,2 

[1] Natl Taiwan Univ, Dept Math, Taipei 10764, Taiwan

[2] Natl Taiwan Univ, Taida Inst Math Sci, Taipei 10764, Taiwan

关键词: Noether's problem;    Rationality problem;    Multiplicative group actions;    Meta-abelian group actions;   

DOI  :  10.1016/j.jalgebra.2009.04.030

来源: Elsevier

【 摘 要 】

Let k be any field. G be a finite group. Theorem. Assume that (i) G contains an abelian normal subgroup H so that G/H is cyclic of order n, (ii) Z vertical bar zeta(n)vertical bar is a unique factorization domain, and (iii) zeta(e) is an element of k where e is the exponent of G, i.e. e = lcm{ord(g): g is an element of G}. If G -> GL(V) is any finite-dimensional linear representation of G over k, then k(V)(G) is rational (= purely transcendental) over k. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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