Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2008-12-01

Journal: FRONTIERS OF MATHEMATICS IN CHINA

Included Journals: Scopus、SCIE

Volume: 3

Issue: 4

Page Number: 555-562

ISSN: 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.