{
  "id": "2302.09513",
  "version": "v1",
  "published": "2023-02-19T09:13:25.000Z",
  "updated": "2023-02-19T09:13:25.000Z",
  "title": "Non-solvable torsion-free virtually solvable groups",
  "authors": [
    "Jonathan A. Hillman"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that a non-solvable, torsion-free, virtually solvable group $S$ must have Hirsch length $h(S)\\geq7$ and either be virtually nilpotent and of nilpotency class $\\leq3$ or have $h(S)\\geq8$. If $S$ is virtually polycyclic but not virtually nilpotent then $h(S)\\geq9$. (There are virtually abelian examples with Hirsch length 15, and this is known to be best possible in the virtually abelian case.)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-19T09:13:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F19"
    ],
    "keywords": [
      "non-solvable torsion-free virtually solvable groups",
      "hirsch length",
      "virtually nilpotent",
      "virtually abelian examples",
      "nilpotency class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}