Invariants of finite groups generated by generalized transvections in the modular case
We investigate the invariant rings of two classes of finite groups which are generated by a number of generalized transvections with an invariant subspace over a finite field 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...