Some zero-sum problems over $\langle x,y \mid x^2 = y^{n/2}, y^n = 1, yx = xy^s \rangle$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915092889600000 |
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| author | Ribas, Sávio |
| author_facet | Ribas, Sávio |
| contents | Let $n \ge 8$ be even, and let $G = \langle x, y \mid x^2 = y^{n/2}, y^n = 1, yx = xy^s \rangle$, where $s^2 \equiv 1 \pmod n$ and $s \not\equiv \pm1 \pmod n$. In this paper, we provide the precise values of some zero-sum constants over $G$, namely the small Davenport constant, $η$-constant, Gao constant, and Erd\H os-Ginzburg-Ziv constant. In particular, the Gao's and Zhuang-Gao's Conjectures hold for $G$. We also solve the associated inverse problems when $n \equiv 0 \pmod 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some zero-sum problems over $\langle x,y \mid x^2 = y^{n/2}, y^n = 1, yx = xy^s \rangle$ Ribas, Sávio Number Theory Combinatorics Let $n \ge 8$ be even, and let $G = \langle x, y \mid x^2 = y^{n/2}, y^n = 1, yx = xy^s \rangle$, where $s^2 \equiv 1 \pmod n$ and $s \not\equiv \pm1 \pmod n$. In this paper, we provide the precise values of some zero-sum constants over $G$, namely the small Davenport constant, $η$-constant, Gao constant, and Erd\H os-Ginzburg-Ziv constant. In particular, the Gao's and Zhuang-Gao's Conjectures hold for $G$. We also solve the associated inverse problems when $n \equiv 0 \pmod 4$. |
| title | Some zero-sum problems over $\langle x,y \mid x^2 = y^{n/2}, y^n = 1, yx = xy^s \rangle$ |
| topic | Number Theory Combinatorics |
| url | https://arxiv.org/abs/2501.03338 |