The Noether Numbers for Cyclic Groups of $pq$ Order in the Modular Case
Received:June 06, 2023  Revised:August 15, 2023
Key Words: Noether number   invariant algebra   cyclic group   modular case  
Fund Project:Supported by the Natural Science Foundation for Young Scientists of China (Grant No.12101375) and the Foundation for Young Scientists of Shanxi Province (Grant No.201901D211184).
Author NameAffiliation
Haixian CHEN School of Mathematical Sciences, Shanxi University, Shanxi 030006, P. R. China 
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Abstract:
      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 $\beta(F[V]^G)$. 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.
Citation:
DOI:10.3770/j.issn:2095-2651.2024.02.003
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