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Indexed by:期刊论文

Date of Publication:2008-12-01

Journal:FRONTIERS OF MATHEMATICS IN CHINA

Included Journals:SCIE、Scopus

Volume:3

Issue:4

Page Number:555-562

ISSN No.:1673-3452

Key Words:Rational invariant; Dickson invariant; rational function field; symplectic group

Abstract:Let F-q be a finite field with q elements, where q is a prime power. Let G be a subgroup of the general linear group over F-q and F-q(x(1), ..., x(n)) be the rational function field over F-q. We seek to understand the structure of the rational invariant subfield F-q(x(1), ..., x(n))(G). In this paper, we prove that F-q(x(1), ..., x(n))(G) is rational (or, purely transcendental) by giving an explicit set of generators when G is the symplectic group. In particular, the set of generators we gave satisfies the Dickson property.