{
  "id": "2107.00491",
  "version": "v1",
  "published": "2021-07-01T14:35:35.000Z",
  "updated": "2021-07-01T14:35:35.000Z",
  "title": "Profinite groups with restricted centralizers of $π$-elements",
  "authors": [
    "Cristina Acciarri",
    "Pavel Shumyatsky"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2003.09933",
  "categories": [
    "math.GR"
  ],
  "abstract": "A group $G$ is said to have restricted centralizers if for each $g$ in $G$ the centralizer $C_G(g)$ either is finite or has finite index in $G$. Shalev showed that a profinite group with restricted centralizers is virtually abelian. Given a set of primes $\\pi$, we take interest in profinite groups with restricted centralizers of $\\pi$-elements. It is shown that such a profinite group has an open subgroup of the form $P\\times Q$, where $P$ is an abelian pro-$\\pi$ subgroup and $Q$ is a pro-$\\pi'$ subgroup. This significantly strengthens a result from our earlier paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-01T14:35:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E18",
      "20F24"
    ],
    "keywords": [
      "profinite group",
      "restricted centralizers",
      "finite index",
      "open subgroup",
      "earlier paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}