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	Noether's problem for the groups with a cyclic subgroup of index 4
	Kang, Ming-Chang ; Michailov, Ivo M. ; Zhou, Jian
	2012
关键词	RETRACT RATIONAL FIELDS GALOIS EXTENSIONS P-GROUPS
英文摘要	Let G be a finite group and k be a field. Let G act on the rational function field k(x (g) : g a G) by k-automorphisms defined by g a (TM) x (h) = x (gh) for any g, h a G. Noether's problem asks whether the fixed field k(G) = k(x (g) : g a G) (G) is rational (i.e., purely transcendental) over k. Theorem 1. If G is a group of order 2 (n) (n >= 4) and of exponent 2 (e) such that (i) e >= n - 2 and (ii) , then k(G) is k-rational. Theorem 2. Let G be a group of order 4n where n is any positive integer (it is unnecessary to assume that n is a power of 2). Assume that (i) char k not equal 2, , and (ii) G contains an element of order n. Then k(G) is rational over k, except for the case n = 2 m and G similar or equal to C (m) a < S C (8) where m is an odd integer and the center of G is of even order (note that C (m) is normal in Cm a < S C (8)); for the exceptional case, k(G) is rational over k if and only if at least one of -1; 2;-2 belongs to (k (x))(2).; Mathematics; SCI(E); 1; ARTICLE; 4; 1037-1058; 17
语种	英语
出处	SCI
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/228916]
专题	数学科学学院
推荐引用方式 GB/T 7714	Kang, Ming-Chang,Michailov, Ivo M.,Zhou, Jian. Noether&apos;s problem for the groups with a cyclic subgroup of index 4. 2012-01-01.

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