In this paper, first we investigate the invariant rings of the finite groups G ≤ GL（n, F;） generated by i-transvections and i-reflections with given invariant subspaces H over a finite field F;in the modular case. ...In this paper, first we investigate the invariant rings of the finite groups G ≤ GL（n, F;） generated by i-transvections and i-reflections with given invariant subspaces H over a finite field F;in the modular case. Then we are concerned with general groups G;（ω） and G;（ω）;named generalized transvection groups where ωis a k-th root of unity. By constructing quotient group and tensor, we calculate their invariant rings. In the end, we determine the properties of Cohen-Macaulay,Gorenstein, complete intersection, polynomial and Poincare series of these rings.展开更多
文摘In this paper, first we investigate the invariant rings of the finite groups G ≤ GL（n, F;） generated by i-transvections and i-reflections with given invariant subspaces H over a finite field F;in the modular case. Then we are concerned with general groups G;（ω） and G;（ω）;named generalized transvection groups where ωis a k-th root of unity. By constructing quotient group and tensor, we calculate their invariant rings. In the end, we determine the properties of Cohen-Macaulay,Gorenstein, complete intersection, polynomial and Poincare series of these rings.
