Loading [MathJax]/jax/output/HTML-CSS/config.js
Journals
Resources
About Us
Open Access

The Invariant Rings of the Generalized Transvection Groups in the Modular Case

The Invariant Rings of the Generalized Transvection Groups in the Modular Case

Year:    2017

Author:    Xiang Han, Jizhu Nan, Ki-Bong Nam

Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 160–176

Abstract

In this paper, first we investigate the invariant rings of the finite groups $G ≤ GL(n, F_q)$ generated by $i$-transvections and $i$-reflections with given invariant subspaces $H$ over a finite field $F_q$ in the modular case. Then we are concerned with general groups $G_i(ω)$ and $G_i(ω)^t$ named generalized transvection groups where $ω$ is a $k$-th root of unity. By constructing quotient group and tensor, we calculate their invariant rings. In the end, we determine the properties of Cohen-Macaulay, Gorenstein, complete intersection, polynomial and Poincare series of these rings.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.13447/j.1674-5647.2017.02.08

Communications in Mathematical Research , Vol. 33 (2017), Iss. 2 : pp. 160–176

Published online:    2017-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    invariant $i$-transvection $i$-reflection generalized transvection group

Author Details

Xiang Han

Jizhu Nan

Ki-Bong Nam