{
  "id": "2203.14534",
  "version": "v1",
  "published": "2022-03-28T07:18:29.000Z",
  "updated": "2022-03-28T07:18:29.000Z",
  "title": "A Combinatorial Proof of a generalization of a Theorem of Frobenius",
  "authors": [
    "Supravat Sarkar"
  ],
  "comment": "Accepted for publication in \"The Mathematics Student\" Journal",
  "categories": [
    "math.GR"
  ],
  "abstract": "In this article, we shall generalize a theorem due to Frobenius in group theory, which asserts that if $p$ is a prime and $p^{r}$ divides the order of a finite group, then the number of subgroups of order $p^{r}$ is $\\equiv$ 1(mod $p$). Interestingly, our proof is purely combinatorial and does not use much group theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-28T07:18:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorial proof",
      "generalization",
      "group theory",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}