{
  "id": "2108.00823",
  "version": "v1",
  "published": "2021-07-16T15:37:38.000Z",
  "updated": "2021-07-16T15:37:38.000Z",
  "title": "The main zero-sum constants over $D_{2n} \\times C_2$",
  "authors": [
    "Fabio Enrique Brochero Martínez",
    "Abílio Lemos",
    "B. K. Moriya",
    "Sávio Ribas"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $C_2$ be the cyclic group of order $2$ and $D_{2n}$ be the dihedral group of order $2n$, where $n$ is even. In this paper, we provide the exact values of some zero-sum constants over $D_{2n} \\times C_2$, namely small Davenport constant, Gao constant, $\\eta$-constant and Erd\\H os-Ginzburg-Ziv constant. As a consequence, we prove the Gao's and Zhuang-Gao's Conjectures for this group. These are the first concrete results on zero-sum problems for a family of non-abelian groups of rank greater than $2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-16T15:37:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B75",
      "11B50",
      "11P70"
    ],
    "keywords": [
      "main zero-sum constants",
      "first concrete results",
      "small davenport constant",
      "non-abelian groups",
      "dihedral group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}