On the separating Noether number of finite abelian groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917959072481280 |
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| author | Schefler, Barna Zhao, Kevin Zhong, Qinghai |
| author_facet | Schefler, Barna Zhao, Kevin Zhong, Qinghai |
| contents | The separating Noether number $β_{\mathrm{sep}}(G)$ 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 $β_{\mathrm{sep}}(G)$, provided that $G$ is either a $p$-group or has rank $2$, $3$ or $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the separating Noether number of finite abelian groups Schefler, Barna Zhao, Kevin Zhong, Qinghai Commutative Algebra Number Theory 13A50, 11B75, 20D60 The separating Noether number $β_{\mathrm{sep}}(G)$ 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 $β_{\mathrm{sep}}(G)$, provided that $G$ is either a $p$-group or has rank $2$, $3$ or $5$. |
| title | On the separating Noether number of finite abelian groups |
| topic | Commutative Algebra Number Theory 13A50, 11B75, 20D60 |
| url | https://arxiv.org/abs/2503.01296 |