Invariants of finite groups generated by generalized transvections in the modular case
| Autor: | Chander Gupta, Jizhu Nan, Xiang Han |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mathematics::Commutative Algebra
Invariant polynomial Root of unity 010102 general mathematics Invariant subspace 01 natural sciences Linear subspace Finite type invariant Combinatorics Finite field 0103 physical sciences 010307 mathematical physics 0101 mathematics Invariant (mathematics) Quotient group Mathematics |
| Zdroj: | Czechoslovak Mathematical Journal. 67:655-698 |
| DOI: | 10.21136/cmj.2017.0044-16 |
| Popis: | We investigate the invariant rings of two classes of finite groups G ≤ 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. |
| Databáze: | OpenAIRE |
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