"simple group" meaning in English

{
  "forms": [
    {
      "form": "simple groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "simple group (plural simple 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": [
        {
          "text": "1989, Roger W. Carter, Simple Groups of Lie Type, John Wiley & Sons, Wiley Classics Edition, page 1,\nSince the first edition of this book was published in 1972, great progress has been made in the theory of finite simple groups. Above all, the classification of the finite simple groups was finally completed in 1981. […] In addition, the five Mathieu groups have been supplemented by the discovery between 1965 and 1981 of 21 further 'sporadic' simple groups."
        },
        {
          "ref": "2000, Michael Aschbacher, Finite Group Theory, 2nd edition, Cambridge University Press, page 260",
          "text": "Let #x5C;mathcal#x7B;K#x7D; be the list of finite simple groups appearing in section 47.[…]\nClassification Theorem. Every finite simple group is isomorphic to a member of #x5C;mathcal#x7B;K#x7D;.",
          "type": "quotation"
        },
        {
          "ref": "2010, John Stillwell, Mathematics and Its History, 3rd edition, Springer, page 495",
          "text": "However, classification of the finite simple groups was much harder than could have been foreseen in the 19th century. It turned out to be easier (though still very hard) to classify continuous simple groups.[…]Each continuous simple group is the symmetry group of a space with hypercomplex coordinates, either from #x5C;mathbb#x7B;R#x7D;, #x5C;mathbb#x7B;C#x7D;, #x5C;mathbb#x7B;H#x7D;, or #x5C;mathbb#x7B;O#x7D;.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A group which has no normal subgroups apart from the trivial group and itself."
      ],
      "id": "en-simple_group-en-noun-Ko7Rcs8H",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group#English"
        ],
        [
          "normal subgroups",
          "normal subgroup#English"
        ],
        [
          "trivial group",
          "trivial group#English"
        ]
      ],
      "raw_glosses": [
        "(group theory) A group which has no normal subgroups apart from the trivial group and itself."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "it",
          "lang": "Italian",
          "sense": "group having no normal subgroups other than the trivial group and itself",
          "tags": [
            "masculine"
          ],
          "word": "gruppo semplice"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "group having no normal subgroups other than the trivial group and itself",
          "tags": [
            "feminine"
          ],
          "word": "grupa prosta"
        }
      ],
      "wikipedia": [
        "simple group"
      ]
    }
  ],
  "word": "simple group"
}

{
  "forms": [
    {
      "form": "simple groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "simple group (plural simple groups)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "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": [
        {
          "text": "1989, Roger W. Carter, Simple Groups of Lie Type, John Wiley & Sons, Wiley Classics Edition, page 1,\nSince the first edition of this book was published in 1972, great progress has been made in the theory of finite simple groups. Above all, the classification of the finite simple groups was finally completed in 1981. […] In addition, the five Mathieu groups have been supplemented by the discovery between 1965 and 1981 of 21 further 'sporadic' simple groups."
        },
        {
          "ref": "2000, Michael Aschbacher, Finite Group Theory, 2nd edition, Cambridge University Press, page 260",
          "text": "Let #x5C;mathcal#x7B;K#x7D; be the list of finite simple groups appearing in section 47.[…]\nClassification Theorem. Every finite simple group is isomorphic to a member of #x5C;mathcal#x7B;K#x7D;.",
          "type": "quotation"
        },
        {
          "ref": "2010, John Stillwell, Mathematics and Its History, 3rd edition, Springer, page 495",
          "text": "However, classification of the finite simple groups was much harder than could have been foreseen in the 19th century. It turned out to be easier (though still very hard) to classify continuous simple groups.[…]Each continuous simple group is the symmetry group of a space with hypercomplex coordinates, either from #x5C;mathbb#x7B;R#x7D;, #x5C;mathbb#x7B;C#x7D;, #x5C;mathbb#x7B;H#x7D;, or #x5C;mathbb#x7B;O#x7D;.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A group which has no normal subgroups apart from the trivial group and itself."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group#English"
        ],
        [
          "normal subgroups",
          "normal subgroup#English"
        ],
        [
          "trivial group",
          "trivial group#English"
        ]
      ],
      "raw_glosses": [
        "(group theory) A group which has no normal subgroups apart from the trivial group and itself."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "simple group"
      ]
    }
  ],
  "translations": [
    {
      "code": "it",
      "lang": "Italian",
      "sense": "group having no normal subgroups other than the trivial group and itself",
      "tags": [
        "masculine"
      ],
      "word": "gruppo semplice"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "group having no normal subgroups other than the trivial group and itself",
      "tags": [
        "feminine"
      ],
      "word": "grupa prosta"
    }
  ],
  "word": "simple group"
}