{
  "id": "1405.7329",
  "version": "v4",
  "published": "2014-05-28T18:41:14.000Z",
  "updated": "2015-06-24T03:46:56.000Z",
  "title": "Characterization of sofic groups and equations over groups",
  "authors": [
    "Lev Glebsky"
  ],
  "comment": "This paper has been withdrawn by the author due to all its results are in 1506.06940. The paper 1506.06940 contains more general and clearly written results",
  "categories": [
    "math.GR"
  ],
  "abstract": "We give the following characterization of sofic (weakly sofic) groups: a group $G$ is sofic (weakly sofic) if and only if any system of equations solvable in any alternating group (any finite group) is solvable over $G$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-29T10:22:16.000Z",
      "comment": "11 pages. It is minor stylistic improvement (I hope) of the version 2. The proof that hyperlinear groups are weakly sofic of the version 1. is wrong and removed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-06-24T03:46:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26",
      "20E18"
    ],
    "keywords": [
      "sofic groups",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.7329G"
    }
  }
}