| Title:
|
Invariants of finite groups generated by generalized transvections in the modular case (English) |
| Author:
|
Han, Xiang |
| Author:
|
Nan, Jizhu |
| Author:
|
Gupta, Chander K. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
67 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
655-698 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the invariant rings of two classes of finite groups $G\leq {\rm GL}(n,F_q)$ which are generated by a number of generalized transvections with an invariant subspace $H$ over a finite field $F_q$ in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned with different invariant subspaces which have the same dimension. We provide a explicit classification of these groups and calculate their invariant rings. (English) |
| Keyword:
|
invariant ring |
| Keyword:
|
transvection |
| Keyword:
|
generalized transvection group |
| MSC:
|
13A50 |
| MSC:
|
20F55 |
| MSC:
|
20F99 |
| idZBL:
|
Zbl 06770123 |
| idMR:
|
MR3697909 |
| DOI:
|
10.21136/CMJ.2017.0044-16 |
| . |
| Date available:
|
2017-09-01T12:21:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146852 |
| . |
| Reference:
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