Davenport constant for finite abelian groups with higher rank
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913235132743680 |
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| author | Biswas, Anamitro Mazumdar, Eshita |
| author_facet | Biswas, Anamitro Mazumdar, Eshita |
| contents | For a finite abelian group $G,$ the Davenport Constant, denoted by $D(G)$, is defined to be the least positive integer $k$ such that every sequence of length at least $k$ has a non-trivial zero-sum subsequence. A long-standing conjecture is that the Davenport constant of a finite abelian group $G =C_{n_1}\times\cdots\times C_{n_d}$ of rank $d \in \mathbb{N}$ is $1+\displaystyle\sum_{i=1}^d (n_i-1) $. This conjecture is false in general, but it remains to know for which groups it is true. In this paper, we consider groups of the form $G = (C_p)^{d-1} \times C_{pq},$ where $p$ is a prime and $q\in \mathbb{N}$ and provide sufficient condition when the conjecture holds true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09999 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Davenport constant for finite abelian groups with higher rank Biswas, Anamitro Mazumdar, Eshita Number Theory 11B75, 11P99, 20K01 For a finite abelian group $G,$ the Davenport Constant, denoted by $D(G)$, is defined to be the least positive integer $k$ such that every sequence of length at least $k$ has a non-trivial zero-sum subsequence. A long-standing conjecture is that the Davenport constant of a finite abelian group $G =C_{n_1}\times\cdots\times C_{n_d}$ of rank $d \in \mathbb{N}$ is $1+\displaystyle\sum_{i=1}^d (n_i-1) $. This conjecture is false in general, but it remains to know for which groups it is true. In this paper, we consider groups of the form $G = (C_p)^{d-1} \times C_{pq},$ where $p$ is a prime and $q\in \mathbb{N}$ and provide sufficient condition when the conjecture holds true. |
| title | Davenport constant for finite abelian groups with higher rank |
| topic | Number Theory 11B75, 11P99, 20K01 |
| url | https://arxiv.org/abs/2402.09999 |