{
  "id": "2407.13606",
  "version": "v1",
  "published": "2024-07-18T15:45:12.000Z",
  "updated": "2024-07-18T15:45:12.000Z",
  "title": "Formations of Finite Groups in Polynomial Time: the $\\mathfrak{F}$-Hypercenter",
  "authors": [
    "Viachaslau I. Murashka"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "For a wide family of formations $\\mathfrak{F}$ (which includes Baer-local formations) it is proved that the $ \\mathfrak{F}$-hypercenter of a permutation finite group can be computed in polynomial time. In particular, the algorithms for computing the $\\mathfrak{F}$-hypercenter for the following classes of groups are suggested: hereditary local formations with the Shemetkov property, rank formations, formations of all quasinilpotent, Sylow tower, $p$-nilpotent, supersoluble, $w$-supersoluble and $SC$-groups. For some of these formations algorithms for the computation of the intersection of all maximal $\\mathfrak{F}$-subgroups are suggested.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-18T15:45:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20B40"
    ],
    "keywords": [
      "polynomial time",
      "hypercenter",
      "hereditary local formations",
      "permutation finite group",
      "baer-local formations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}