Invariants of finite groups generated by generalized transvections in the modular case

Han, Xiang   ; Nan, Jizhu   ; Gupta, Chander K.

Czechoslovak Mathematical Journal, Tome 67 (2017) no. 3, pp. 655-698

Abstract (VO)

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.

Détail

DOI : 10.21136/CMJ.2017.0044-16

Classification : 13A50, 20F55, 20F99
Keywords: invariant ring; transvection; generalized transvection group

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