Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2017-09-01

Journal: CZECHOSLOVAK MATHEMATICAL JOURNAL

Included Journals: SCIE、Scopus

Volume: 67

Issue: 3

Page Number: 655-698

ISSN: 0011-4642

Key Words: invariant ring; transvection; generalized transvection group

Abstract: We investigate the invariant rings of two classes of finite groups G GL(n, F (q)) which are generated by a number of generalized transvections with an invariant subspace H over a finite field F (q) in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned with different invariant subspaces which have the same dimension. We provide a explicit classification of these groups and calculate their invariant rings.