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Indexed by:期刊论文

Date of Publication:2017-09-01

Journal:CZECHOSLOVAK MATHEMATICAL JOURNAL

Included Journals:Scopus、SCIE

Volume:67

Issue:3

Page Number:655-698

ISSN No.: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.