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.
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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