TY - JOUR
T1 - The Invariant Rings of the Generalized Transvection Groups in the Modular Case
AU - Han , Xiang
AU - Nan , Jizhu
AU - Nam , Ki-Bong
JO - Communications in Mathematical Research 
VL - 2
SP - 160
EP - 176
PY - 2019
DA - 2019/11
SN - 33
DO - http://doi.org/10.13447/j.1674-5647.2017.02.08
UR - https://global-sci.org/intro/article_detail/cmr/13396.html
KW - invariant, $i$-transvection, $i$-reflection, generalized transvection group
AB - <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>