A note on a Conjecture of Gao and Zhuang for groups of order $27$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913294516748288 |
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| author | Godara, Naveen K. Sarkar, Siddhartha |
| author_facet | Godara, Naveen K. Sarkar, Siddhartha |
| contents | The small Davenport constant ${\mathsf{d}}(G)$ of a finite group $G$ is defined to be the maximal length of a sequence over $G$ which has no non-trivial product-one subsequence. In this paper, we prove that ${\mathsf{d}}(G) = 6$ for the non-abelian group of order $27$ and exponent $3$ and thereby establish a conjecture by Gao and Zhuang for this group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_02387 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on a Conjecture of Gao and Zhuang for groups of order $27$ Godara, Naveen K. Sarkar, Siddhartha Group Theory Primary 20D60, Secondary 11B75 The small Davenport constant ${\mathsf{d}}(G)$ of a finite group $G$ is defined to be the maximal length of a sequence over $G$ which has no non-trivial product-one subsequence. In this paper, we prove that ${\mathsf{d}}(G) = 6$ for the non-abelian group of order $27$ and exponent $3$ and thereby establish a conjecture by Gao and Zhuang for this group. |
| title | A note on a Conjecture of Gao and Zhuang for groups of order $27$ |
| topic | Group Theory Primary 20D60, Secondary 11B75 |
| url | https://arxiv.org/abs/2311.02387 |