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

Xiang Han; Jizhu Nan; Chander K. Gupta — 2017

Czechoslovak Mathematical Journal

We investigate the invariant rings of two classes of finite groups $G \leq GL (n, F_{q})$ 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...

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