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.
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Received: 14.12.1998
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Domokos, M., Hegedűs, P. Noether's bound for polynomial invariants of finite groups. Arch. Math. 74, 161–167 (2000). https://doi.org/10.1007/s000130050426
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DOI: https://doi.org/10.1007/s000130050426