A note on a Conjecture of Gao and Zhuang for groups of order $27$
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913294516748288 |
|---|---|
| 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 |
| id |
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 |