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.

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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

Author Details

Xiang Han

Jizhu Nan

Ki-Bong Nam