{
  "id": "2311.02387",
  "version": "v1",
  "published": "2023-11-04T12:04:00.000Z",
  "updated": "2023-11-04T12:04:00.000Z",
  "title": "A note on a Conjecture of Gao and Zhuang for groups of order $27$",
  "authors": [
    "Naveen K. Godara",
    "Siddhartha Sarkar"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "The small Davenport constant ${\\mathsf{d}}(G)$ is defined to be the maximal length of a product-one free non-trivial sequence in a finite group $G$. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-04T12:04:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "11B75"
    ],
    "keywords": [
      "conjecture",
      "product-one free non-trivial sequence",
      "small davenport constant",
      "finite group",
      "maximal length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}