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

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Abstract

We investigate the invariant rings of two classes of finite groups G ≤ GL(n, Fq) which are generated by a number of generalized transvections with an invariant subspace H over a finite field Fq 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.

Keywords

invariant ring transvection generalized transvection group 

MSC 2010

13A50 20F55 20F99 

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© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyGanjingzi, LiaoningP.R. China
  2. 2.Department of MathematicsUniversity of ManitobaWinnipegCanada

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