{
  "id": "2205.12913",
  "version": "v1",
  "published": "2022-05-25T17:06:10.000Z",
  "updated": "2022-05-25T17:06:10.000Z",
  "title": "Formations of Finite Groups in Polynomial Time: $\\mathfrak{F}$-residuals and $\\mathfrak{F}$-subnormality",
  "authors": [
    "Viachaslau I. Murashka"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "For a wide family of formations $\\mathfrak{F}$ it is proved that the $ \\mathfrak{F}$-residual of a permutation finite group can be computed in a polynomial time. Moreover, if in the previous case $\\mathfrak{F}$ is hereditary, then an $\\mathfrak{F}$-subnormality of a subgroup can be checked in a polynomial time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-25T17:06:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D10",
      "20B40"
    ],
    "keywords": [
      "polynomial time",
      "formations",
      "subnormality",
      "permutation finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}