| 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
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| 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). |
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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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