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


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.


Finite Group Cyclic Group Prime Order Polynomial Algebra Polynomial Invariant 
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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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