{
  "id": "2010.04808",
  "version": "v1",
  "published": "2020-10-09T21:10:36.000Z",
  "updated": "2020-10-09T21:10:36.000Z",
  "title": "Finite groups whose maximal subgroups of order divisible by all the primes are supersolvable",
  "authors": [
    "Alexander Moretó"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We study finite groups $G$ with the property that for any subgroup $M$ maximal in $G$ whose order is divisible by all the prime divisors of $|G|$, $M$ is supersolvable. We show that any nonabelian simple group can occur as a composition factor of such a group and that, if $G$ is solvable, then the nilpotency length and the rank are arbitrarily large. On the other hand, for every prime $p$, the $p$-length of such a group is at most $1$. This answers questions proposed by V. Monakhov in The Kourovka Notebook.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T21:10:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20F16"
    ],
    "keywords": [
      "maximal subgroups",
      "order divisible",
      "study finite groups",
      "nonabelian simple group",
      "supersolvable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}