{
  "id": "enwiki-001372340707",
  "slug": "malnormal-subgroup",
  "title": "Malnormal subgroup",
  "qid": "",
  "lead": "In group theory, a subgroup H of a group G is termed malnormal if for any group element x not in H , H and xHx^{-1} intersect only in the identity element. Some facts about malnormality: * The intersection of malnormal subgroups is malnormal. * Malnormality is transitive; that is, a malnormal subgroup of a malnormal subgroup is malnormal. * The trivial subgroup and the whole group are malnormal subgroups. A normal subgroup that is also malnormal must be one of these. * Every malnormal subgroup is a special type of C-group called a trivial intersection subgroup, or TI subgroup. When G is finite, a malnormal subgroup H distinct from 1 and G is called a \"Frobenius complement\". The set N of elements of G which are either equal to 1 or non-conjugate to any element of H is a normal subgroup of G , called the \"Frobenius kernel\", and G is the semidirect product of H and N .",
  "body": "In group theory, a subgroup H of a group G is termed malnormal if for any group element x not in H , H and xHx^{-1} intersect only in the identity element. Some facts about malnormality: The intersection of malnormal subgroups is malnormal. Malnormality is transitive; that is, a malnormal subgroup of a malnormal subgroup is malnormal. The trivial subgroup and the whole group are malnormal subgroups. A normal subgroup that is also malnormal must be one of these. Every malnormal subgroup is a special type of C-group called a trivial intersection subgroup, or TI subgroup. When G is finite, a malnormal subgroup H distinct from 1 and G is called a \"Frobenius complement\". The set N of elements of G which are either equal to 1 or non-conjugate to any element of H is a normal subgroup of G , called the \"Frobenius kernel\", and G is the semidirect product of H and N . ==Notes== ==References==",
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  "license": "CC BY-SA 4.0",
  "source_uri": "https://en.wikipedia.org/w/index.php?oldid=1372340707",
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    "id": "enwiki-001372340707",
    "type": "webpage",
    "title": "Malnormal subgroup",
    "author": [
      {
        "family": "Anticloud FZ LLE",
        "literal": "Anticloud FZ LLE"
      }
    ],
    "container-title": "encyclopegia.org",
    "publisher": "Anticloud FZ LLE",
    "publisher-place": "Dubai, United Arab Emirates",
    "URL": "https://encyclopegia.org/a/malnormal-subgroup",
    "issued": {
      "date-parts": [
        [
          2026,
          11,
          15
        ]
      ]
    },
    "accessed": {
      "date-parts": [
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          2026,
          11,
          15
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    "license": "CC BY-SA 4.0",
    "DOI": "eo1:enwiki-001372340707",
    "isBasedOn": "https://en.wikipedia.org/w/index.php?oldid=1372340707",
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