Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-03-01

Journal: ALGEBRA COLLOQUIUM

Included Journals: Scopus、SCIE

Volume: 19

Issue: 1

Page Number: 149-158

ISSN: 1005-3867

Key Words: maximal subgroup; rational invariant; polynomial invariant

Abstract: The maximal subgroups of the finite classical groups are divided into nine classes by Aschbacher's theorem. In this paper, we give explicit transcendental bases of the invariant subfields of those maximal subgroups of classical groups of linear, symplectic and unitary cases that lie in the first two of these classes. Also, we show that the invariant rings of the maximal subgroups of the finite linear groups that lie in the first class are polynomial rings.