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Archiv der Mathematik

, Volume 74, Issue 3, pp 161–167 | Cite as

Noether's bound for polynomial invariants of finite groups

  • M. Domokos
  • P. Hegedűs

Abstract.

Let G be a finite group acting linearly on the polynomial algebra \(\Bbb C [V]\). We prove that if G is the semi-direct product of cyclic groups of odd prime order, then the algebra of polynomial invariants is generated by its elements whose degree is bounded by \({5 \over 8}|G|\). As a consequence we derive that \(\Bbb C [V]^G\) is generated by elements of degree \(\leqq {3 \over 4}|G|\) for any non-cyclic group G. This sharpens the improved bound for Noether's Theorem due to Schmid.

Keywords

Finite Group Cyclic Group Prime Order Polynomial Algebra Polynomial Invariant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • M. Domokos
    • 1
  • P. Hegedűs
    • 2
  1. 1.Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, HungaryHU
  2. 2.Department of Algebra and Number Theory, Eötvös University, Budapest, Múzeum krt 6 – 8, H-1088, HungaryHU

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