The Invariant Rings of the Generalized Transvection Groups in the Modular Case |
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Authors: | HAN XIANG NAN JI-ZHU NAM KI-BONG |
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Affiliation: | 1. School of Mathematical Sciences, Dalian University of Technology, Liaoning, 116024;2. Department of Mathematics and Computer Science, University of Wisconsin-Whitewater, Whitewater, WI 53190, United States |
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Abstract: | In this paper, first we investigate the invariant rings of the finite groups G ≤ GL(n, Fq ) generated by i-transvections and i-reflections with given invariant subspaces H over a finite field Fq in the modular case. Then we are concerned with general groups Gi(ω) and Gi(ω)t 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. |
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Keywords: | invariant i-transvection i-reflection generalized transvection group |
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