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	The rationality problem for finite subgroups of GL(4)(Q)
	Kang, Ming-chang ; Zhou, Jian
	2012
关键词	Rationality problem Rationality Retract rationality Conic bundles NOETHERS PROBLEM LINEAR ACTIONS
英文摘要	Let G be a finite subgroup of GL(4)(Q). The group G induces an action on Q(x(1) x(2), x(3), x(4)), the rational function field of four variables over Q. Theorem. The fixed subfield Q(x(1), x(2), x(3), x(4))(G) := {f is an element of Q(x(1), x(2), x(3), x(4)): sigma . f = f for any sigma is an element of G} is rational (i.e. purely transcendental) over Q, except for two groups which are images of faithful representations of C-8 and C-3 (sic) C-8 into GL(4)(Q) (both fixed fields for these two exceptional cases are not rational over Q). There are precisely 227 such groups in GL(4)(Q) up to conjugation; the answers to the rationality problem for most of them were proved by Kitayama and Yamasaki (2009) [KY] except for four cases. We solve these four cases left unsettled by Kitayama and Yamasaki; thus the whole problem is solved completely. (c) 2012 Elsevier Inc. All rights reserved.; Mathematics; SCI(E); 2; ARTICLE; 53-69; 368
语种	英语
出处	SCI
出版者	journal of algebra
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/229897]
专题	数学科学学院
推荐引用方式 GB/T 7714	Kang, Ming-chang,Zhou, Jian. The rationality problem for finite subgroups of GL(4)(Q). 2012-01-01.

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