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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, F q) 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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, No. 2 Linggong Road, Dalian, 116024, Ganjingzi, Liaoning, P.R. China

    Xiang Han & Jizhu Nan

  2. Department of Mathematics, University of Manitoba, Machray Hall 420, 186 Dysart Rd, Winnipeg, MB, R3T 2M8, Canada

    Chander K. Gupta

Authors
  1. Xiang Han
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  2. Jizhu Nan
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  3. Chander K. Gupta
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Corresponding author

Correspondence to Xiang Han.

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 11371343).

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Han, X., Nan, J. & Gupta, C.K. Invariants of finite groups generated by generalized transvections in the modular case. Czech Math J 67, 655–698 (2017). https://doi.org/10.21136/CMJ.2017.0044-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0044-16

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