{
  "id": "1111.5216",
  "version": "v2",
  "published": "2011-11-22T15:15:19.000Z",
  "updated": "2012-09-08T13:01:47.000Z",
  "title": "Characterization of cyclic Schur groups",
  "authors": [
    "Sergei Evdokimov",
    "István Kovács",
    "Ilya Ponomarenko"
  ],
  "comment": "the second version; the proof was substantially improved; 29 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A finite group $G$ is called a Schur group, if any Schur ring over $G$ is the transitivity module of a permutation group on the set $G$ containing the regular subgroup of all right translations. It was proved by R. P\\\"oschel (1974) that given a prime $p\\ge 5$ a $p$-group is Schur if and only if it is cyclic. We prove that a cyclic group of order $n$ is a Schur group if and only if $n$ belongs to one of the following five (partially overlapped) families of integers: $p^k$, $pq^k$, $2pq^k$, $pqr$, $2pqr$ where $p,q,r$ are distinct primes, and $k\\ge 0$ is an integer.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-08T13:01:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "20B25"
    ],
    "keywords": [
      "cyclic schur groups",
      "characterization",
      "distinct primes",
      "cyclic group",
      "transitivity module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.5216E"
    }
  }
}