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论文类型：期刊论文

发表时间：2017-09-01

发表刊物：CZECHOSLOVAK MATHEMATICAL JOURNAL

收录刊物：Scopus、SCIE

卷号：67

期号：3

页面范围：655-698

ISSN号：0011-4642

关键字：invariant ring; transvection; generalized transvection group

摘要：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.