{
  "id": "1601.01679",
  "version": "v1",
  "published": "2016-01-07T20:15:10.000Z",
  "updated": "2016-01-07T20:15:10.000Z",
  "title": "More on regular subgroups of the affine group",
  "authors": [
    "M. A. Pellegrini",
    "M. C. Tamburini Bellani"
  ],
  "categories": [
    "math.GR",
    "math.RA"
  ],
  "abstract": "This paper is a new contribution to the study of regular subgroups of the affine group $AGL_n(F)$, for any field $F$. In particular we associate to any partition $\\lambda\\neq (1^{n+1})$ of $n+1$ abelian regular subgroups in such a way that different partitions define non-conjugate subgroups. Moreover, we classify the regular subgroups of certain natural types for $n\\leq 4$. Our classification is equivalent to the classification of split local algebras of dimension $n+1$ over $F$. Our methods, based on classical results of linear algebra, are computer free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-07T20:15:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A21",
      "20B35",
      "16L99"
    ],
    "keywords": [
      "affine group",
      "partitions define non-conjugate subgroups",
      "split local algebras",
      "abelian regular subgroups",
      "computer free"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160101679P"
    }
  }
}