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The Noether Numbers for Cyclic Groups of pq Order in the Modular Case
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Let G be a cyclic group of order pq,where q|p-1,q,p are prime numbers and let F be a field of characteristic p.Let V be a finite-dimensional G-module over F.We refer to the maximal degree of indecomposable polynomials in the invariant algebra F[V]G as the Noether number of the invariant algebra F[V]G,denoted β(F[V]G).In this paper,we determine the Noether number of the invariant algebra F[V]G.Furthermore,we prove that for such a cyclic group of order pq,Wehlau's conjecture holds.
Noether numberinvariant algebracyclic groupmodular case
Haixian CHEN
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School of Mathematical Sciences,Shanxi University,Shanxi 030006,P.R.China
Natural Science Foundation for Young Scientists of ChinaFoundation for Young Scientists of Shanxi Province
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