Title: On the separating Noether number of finite abelian groups Show Chinese title

Title: 关于有限交换群的分离诺特数

Abstract: The separating Noether number $\beta_{\mathrm{sep}}(G)$ of a finite group $G$ is the minimal positive integer $d$ such that for every finite $G$-module $V$ there is a separating set consisting of invariant polynomials of degree at most $d$. In this paper we use methods from additive combinatorics to investigate the separating Noether number for finite abelian groups. Among others, we obtain the exact value of $\beta_{\mathrm{sep}}(G)$, provided that $G$ is either a $p$-group or has rank $2$, $3$ or $5$. Show Chinese abstract

Abstract: 分离诺特数$\beta_{\mathrm{sep}}(G)$的有限群$G$是最小的正整数$d$，使得对于每个有限$G$-模$V$，存在一个由不变多项式的分离集，其次数不超过$d$。在本文中，我们使用加法组合学的方法来研究有限交换群的分离诺特数。 在其他结果中，我们得到了$\beta_{\mathrm{sep}}(G)$的精确值，前提是$G$是一个$p$-群或者其秩为$2$，$3$或者$5$。