Abstract. We investigate the invariant rings of two classes of finite groups G 6 GL(n,Fq)
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.

EB00000003290K

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• INVARIANTS OF FINITE GROUPS GENERATED BY GENERALIZED TRANSVECTIONS IN THE MODULAR CASE