@Article{CMR-33-2,
author = {Xiang, Han and Nan, Jizhu and Nam, Ki-Bong},
title = {The Invariant Rings of the Generalized Transvection Groups in the Modular Case},
journal = {Communications in Mathematical Research },
year = {2017},
volume = {33},
number = {2},
pages = {160--176},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.13447/j.1674-5647.2017.02.08},
url = {https://global-sci.com/article/81644/the-invariant-rings-of-the-generalized-transvection-groups-in-the-modular-case}
}