Davenport constant and its variants for some non-abelian groups
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909223321862144 |
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| author | Babu, C. G. Karthick Bera, Ranjan Ghosh, Mainak Sury, B. |
| author_facet | Babu, C. G. Karthick Bera, Ranjan Ghosh, Mainak Sury, B. |
| contents | We define two variants $e(G)$, $f(G)$ of the Davenport constant $d(G)$ of a finite group $G$, that is not necessarily abelian. These naturally arising constants aid in computing $d(G)$ and are of potential independent interest. We compute the constants $d(G)$, $e(G)$, $f(G)$ for some nonabelian groups G, and demonstrate that, unlike abelian groups where these constants are identical, they can each be distinct. As a byproduct of our results, we also obtain some cases of a conjecture of J. Bass. We compute the $k$-th Davenport constant for several classes of groups as well. We also make a conjecture on $f(G)$ for metacyclic groups and provide evidence towards it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09210 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Davenport constant and its variants for some non-abelian groups Babu, C. G. Karthick Bera, Ranjan Ghosh, Mainak Sury, B. Combinatorics Number Theory 20D60, 11B75, 11P70 We define two variants $e(G)$, $f(G)$ of the Davenport constant $d(G)$ of a finite group $G$, that is not necessarily abelian. These naturally arising constants aid in computing $d(G)$ and are of potential independent interest. We compute the constants $d(G)$, $e(G)$, $f(G)$ for some nonabelian groups G, and demonstrate that, unlike abelian groups where these constants are identical, they can each be distinct. As a byproduct of our results, we also obtain some cases of a conjecture of J. Bass. We compute the $k$-th Davenport constant for several classes of groups as well. We also make a conjecture on $f(G)$ for metacyclic groups and provide evidence towards it. |
| title | Davenport constant and its variants for some non-abelian groups |
| topic | Combinatorics Number Theory 20D60, 11B75, 11P70 |
| url | https://arxiv.org/abs/2406.09210 |