{
  "id": "0708.2391",
  "version": "v2",
  "published": "2007-08-17T16:18:46.000Z",
  "updated": "2009-01-19T20:17:27.000Z",
  "title": "On the capability of finite groups of class two and prime exponent",
  "authors": [
    "Arturo Magidin"
  ],
  "comment": "43 pp; incorporates results from older paper; fix amsrefs/hyperref incompatibility and a typo",
  "categories": [
    "math.GR"
  ],
  "abstract": "We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of some old results and several new ones. In particular, we establish a number of new necessary and new sufficient conditions for capability, including a sufficient condition based only on the ranks of $G/Z(G)$ and $[G,G]$. Finally, we characterise the capable groups among the 5-generated groups in this class.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-19T20:17:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20F12"
    ],
    "keywords": [
      "finite groups",
      "capability",
      "sufficient condition",
      "odd prime exponent",
      "vector spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2391M"
    }
  }
}