# 澳门新葡8455最新网站,www.8455.com,新葡京最新官网

Invariants of Finite Groups Generated by Generalized Transvections in the Modular Case

In this talk, we investigate the invariant rings of two classes of finite groups $G\leq GL(n,F_q)$ that are generated by a number of generalized transvections with invariant subspaces $H$ over a finite field $F_q$ in the modular case. We name these groups by generalized transvection groups. The one class is concerned with a given invariant subspace which is involved several roots of unity. Constructing quotient group and tensor, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other one is concerned with different invariant subspaces which have same dimension. We provide a classification of these groups and illustrate their invariant rings in detail.