{
  "id": "enwiki-001170056780",
  "slug": "perfect-core",
  "title": "Perfect core",
  "qid": "",
  "lead": "In mathematics, in the field of group theory, the perfect core (or perfect radical) of a group is its largest perfect subgroup. Its existence is guaranteed by the fact that the subgroup generated by a family of perfect subgroups is again a perfect subgroup. The perfect core is also the point where the transfinite derived series stabilizes for any group. A group whose perfect core is trivial is termed a hypoabelian group. Every solvable group is hypoabelian, and so is every free group. More generally, every residually solvable group is hypoabelian. The quotient of a group G by its perfect core is hypoabelian, and is called the hypoabelianization of G.",
  "body": "In mathematics, in the field of group theory, the perfect core (or perfect radical) of a group is its largest perfect subgroup. Its existence is guaranteed by the fact that the subgroup generated by a family of perfect subgroups is again a perfect subgroup. The perfect core is also the point where the transfinite derived series stabilizes for any group. A group whose perfect core is trivial is termed a hypoabelian group. Every solvable group is hypoabelian, and so is every free group. More generally, every residually solvable group is hypoabelian. The quotient of a group G by its perfect core is hypoabelian, and is called the hypoabelianization of G. ==References==",
  "categories": [
    "23468805",
    "28607426",
    "28691675",
    "29176626",
    "32448602"
  ],
  "license": "CC BY-SA 4.0",
  "source_uri": "https://en.wikipedia.org/w/index.php?oldid=1170056780",
  "content_hash": "",
  "created_at": null,
  "updated_at": 1691875992.0,
  "claims": [],
  "contradictions": [],
  "confidence": 0.6,
  "csl": {
    "id": "enwiki-001170056780",
    "type": "webpage",
    "title": "Perfect core",
    "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/perfect-core",
    "issued": {
      "date-parts": [
        [
          2026,
          11,
          15
        ]
      ]
    },
    "accessed": {
      "date-parts": [
        [
          2026,
          11,
          15
        ]
      ]
    },
    "license": "CC BY-SA 4.0",
    "DOI": "eo1:enwiki-001170056780",
    "isBasedOn": "https://en.wikipedia.org/w/index.php?oldid=1170056780",
    "note": "Immutable snapshot enwiki-001170056780"
  }
}