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 $G$-module $V$ there is a separating set of degree $\leq d$. In this manuscript, we investigate the separating Noether number $\beta_{\mathrm{sep}}(G)$. Among others, we obtain the exact value of $\beta_{\mathrm{sep}}(G)$ for finite abelian groups $G$, when either $G$ is a $p$-group or $\mathsf r(G)\in \{3,5\}$. Show Chinese abstract

Abstract: 有限群$G$的分离 Noether 数$\beta_{\mathrm{sep}}(G)$是最小的正整数$d$，使得对于每个$G$模块$V$，存在一个度数为$\leq d$的分离集。 在本文中，我们研究分离 Noether 数$\beta_{\mathrm{sep}}(G)$。 在其他结果中，我们得到了有限交换群$G$中$\beta_{\mathrm{sep}}(G)$的精确值，当$G$是$p$-群或$\mathsf r(G)\in \{3,5\}$时。