"sporadic group" meaning in English

{
  "etymology_text": "The earliest usage is thought to be that of English mathematician William Burnside in 1911, W. Burnside, Theory of Groups of Finite Order, 2nd Edition, in a comment about the Mathieu groups.",
  "forms": [
    {
      "form": "sporadic groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "sporadic group (plural sporadic groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1998, Meinolf Geck, “Finite Groups of Lie Type”, in Roger William Carter, Meinolf Geck, editors, Representations of Reductive Groups, Cambridge University Press, page 63",
          "text": "By the classification of finite simple groups in 1981 it is now known that every finite simple group is either cyclic of prime order, or an alternating group of degree 5 or bigger, or a simple group of Lie type as above, or one of 26 sporadic groups.",
          "type": "quotation"
        },
        {
          "ref": "1998, David J. Benson, “Cohomology of Sporadic Groups, Finite Loop Spaces, and the Dickson Invariants”, in Peter H. Kropholler, Graham A. Niblo, Ralph Stöhr, editors, Geometry and Cohomology in Group Theory, Cambridge University Press, page 10",
          "text": "The first five sporadic groups were discovered by Mathieu in the late nineteenth century. The remaining twenty-one were discovered in the nineteen sixties and seventies.",
          "type": "quotation"
        },
        {
          "ref": "2004, Alejandro Adem, R. James Milgram, Cohomology of Finite Groups, 2nd edition, Springer, page 245",
          "text": "It is natural to expect that the sporadic groups should play a role in the structure of the Coker(J) space, though we are only beginning to understand some of the smaller sporadic groups in this framework.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any one of the 26 exceptional finite simple groups, which do not belong to any of the general, infinite categories specified by the classification theorem for finite simple groups."
      ],
      "hyponyms": [
        {
          "sense": "exceptional finite simple group",
          "word": "baby monster group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Conway group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Fischer group"
        },
        {
          "english": "= monster group",
          "sense": "exceptional finite simple group",
          "word": "Fischer–Griess monster group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Harada–Norton group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Held group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Janko group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Lyons group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "McLaughlin group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Mathieu group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "monster group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Higman–Sims group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "O'Nan group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "pariah group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Rudvalis group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Suzuki group"
        },
        {
          "sense": "exceptional finite simple group",
          "word": "Thompson group"
        }
      ],
      "id": "en-sporadic_group-en-noun-uChxan2Z",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "exceptional",
          "exceptional"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "simple group",
          "simple group"
        ]
      ],
      "raw_glosses": [
        "(group theory) Any one of the 26 exceptional finite simple groups, which do not belong to any of the general, infinite categories specified by the classification theorem for finite simple groups."
      ],
      "related": [
        {
          "word": "happy family"
        }
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Mathieu groups",
        "William Burnside",
        "sporadic group"
      ]
    }
  ],
  "word": "sporadic group"
}

{
  "etymology_text": "The earliest usage is thought to be that of English mathematician William Burnside in 1911, W. Burnside, Theory of Groups of Finite Order, 2nd Edition, in a comment about the Mathieu groups.",
  "forms": [
    {
      "form": "sporadic groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "sporadic group (plural sporadic groups)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "sense": "exceptional finite simple group",
      "word": "baby monster group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Conway group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Fischer group"
    },
    {
      "english": "= monster group",
      "sense": "exceptional finite simple group",
      "word": "Fischer–Griess monster group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Harada–Norton group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Held group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Janko group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Lyons group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "McLaughlin group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Mathieu group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "monster group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Higman–Sims group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "O'Nan group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "pariah group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Rudvalis group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Suzuki group"
    },
    {
      "sense": "exceptional finite simple group",
      "word": "Thompson group"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "happy family"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Group theory"
      ],
      "examples": [
        {
          "ref": "1998, Meinolf Geck, “Finite Groups of Lie Type”, in Roger William Carter, Meinolf Geck, editors, Representations of Reductive Groups, Cambridge University Press, page 63",
          "text": "By the classification of finite simple groups in 1981 it is now known that every finite simple group is either cyclic of prime order, or an alternating group of degree 5 or bigger, or a simple group of Lie type as above, or one of 26 sporadic groups.",
          "type": "quotation"
        },
        {
          "ref": "1998, David J. Benson, “Cohomology of Sporadic Groups, Finite Loop Spaces, and the Dickson Invariants”, in Peter H. Kropholler, Graham A. Niblo, Ralph Stöhr, editors, Geometry and Cohomology in Group Theory, Cambridge University Press, page 10",
          "text": "The first five sporadic groups were discovered by Mathieu in the late nineteenth century. The remaining twenty-one were discovered in the nineteen sixties and seventies.",
          "type": "quotation"
        },
        {
          "ref": "2004, Alejandro Adem, R. James Milgram, Cohomology of Finite Groups, 2nd edition, Springer, page 245",
          "text": "It is natural to expect that the sporadic groups should play a role in the structure of the Coker(J) space, though we are only beginning to understand some of the smaller sporadic groups in this framework.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any one of the 26 exceptional finite simple groups, which do not belong to any of the general, infinite categories specified by the classification theorem for finite simple groups."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "exceptional",
          "exceptional"
        ],
        [
          "finite",
          "finite"
        ],
        [
          "simple group",
          "simple group"
        ]
      ],
      "raw_glosses": [
        "(group theory) Any one of the 26 exceptional finite simple groups, which do not belong to any of the general, infinite categories specified by the classification theorem for finite simple groups."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Mathieu groups",
        "William Burnside",
        "sporadic group"
      ]
    }
  ],
  "word": "sporadic group"
}