The Noether Numbers for Cyclic Groups of pq Order in the Modular Case  

作　　者：Haixian CHEN 

机构地区：[1]School of Mathematical Sciences,Shanxi University,Shanxi 030006,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第2期161-169,共9页数学研究及应用（英文版）

基　　金：Supported by the Natural Science Foundation for Young Scientists of China(Grant No.12101375);the Foundation for Young Scientists of Shanxi Province(Grant No.201901D211184).

摘　　要：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),denotedβ(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.

关 键 词：Noether number invariant algebra cyclic group modular case 

分 类 号：O152[理学—数学]