{
  "id": "2204.05497",
  "version": "v1",
  "published": "2022-04-12T03:10:47.000Z",
  "updated": "2022-04-12T03:10:47.000Z",
  "title": "A note on $d$-maximal $p$-groups I",
  "authors": [
    "Messab Aiech",
    "Hanifa Zekraoui",
    "Yassine Guerboussa"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A finite $p$-group $G$ is said to be $d$-maximal if $d(H)<d(G)$ for every subgroup $H<G$, where $d(G)$ denotes the minimal number of generators of $G$. A similar definition can be formulated when $G$ is acted on by some group $A$. We generalize results of B. Kahn and T. Laffey to the latter case, and give them in particular alternative short proofs. We answer moreover a question of Y. Berkovich about the minimal non-metacyclic $p$-groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-12T03:10:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15"
    ],
    "keywords": [
      "minimal number",
      "similar definition",
      "alternative short proofs",
      "minimal non-metacyclic",
      "generators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}