{
  "id": "2204.03368",
  "version": "v1",
  "published": "2022-04-07T11:33:03.000Z",
  "updated": "2022-04-07T11:33:03.000Z",
  "title": "On recognition of $A_6\\times A_6$ by the set of conjugacy class sizes",
  "authors": [
    "Viktor Panshin"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "For a finite group $G$ denote by $N(G)$ the set of conjugacy class sizes of $G$. Recently the following question has been asked: Is it true that for each nonabelian finite simple group $S$ and each $n\\in\\mathbb{N}$, if the set of class sizes of a finite group $G$ with trivial center is the same as the set of class sizes of the direct power $S^n$, then $G\\simeq S^n$? In this paper we approach an answer to this question by proving that $A_6\\times A_6$ is uniquely determined by $N(A_6\\times A_6)$ among finite groups with trivial center.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-07T11:33:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "20D60"
    ],
    "keywords": [
      "conjugacy class sizes",
      "finite group",
      "trivial center",
      "recognition",
      "nonabelian finite simple group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}