"symmetric group" meaning in English

{
  "forms": [
    {
      "form": "symmetric groups",
      "tags": [
        "plural"
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    }
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  "head_templates": [
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      "args": {},
      "expansion": "symmetric group (plural symmetric groups)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
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            "Entries with incorrect language header",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
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            "Fundamental"
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        }
      ],
      "glosses": [
        "A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections."
      ],
      "id": "en-symmetric_group-en-noun-7DyUdyk7",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "group",
          "group"
        ],
        [
          "element",
          "element"
        ],
        [
          "bijection",
          "bijection"
        ],
        [
          "set",
          "set"
        ],
        [
          "operation",
          "operation"
        ],
        [
          "composition",
          "composition"
        ]
      ],
      "meronyms": [
        {
          "word": "alternating group"
        }
      ],
      "raw_glosses": [
        "(mathematics) A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "mathematics: a group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections",
          "word": "symmetrinen ryhmä"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "mathematics: a group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections",
          "tags": [
            "feminine"
          ],
          "word": "samhverf grúpa"
        }
      ],
      "wikipedia": [
        "symmetric group"
      ]
    }
  ],
  "word": "symmetric group"
}

{
  "forms": [
    {
      "form": "symmetric groups",
      "tags": [
        "plural"
      ]
    }
  ],
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  "lang_code": "en",
  "meronyms": [
    {
      "word": "alternating group"
    }
  ],
  "pos": "noun",
  "senses": [
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        "English countable nouns",
        "English entries with incorrect language header",
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        "Terms with Finnish translations",
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        "en:Mathematics"
      ],
      "glosses": [
        "A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "group",
          "group"
        ],
        [
          "element",
          "element"
        ],
        [
          "bijection",
          "bijection"
        ],
        [
          "set",
          "set"
        ],
        [
          "operation",
          "operation"
        ],
        [
          "composition",
          "composition"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "symmetric group"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "mathematics: a group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections",
      "word": "symmetrinen ryhmä"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "mathematics: a group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections",
      "tags": [
        "feminine"
      ],
      "word": "samhverf grúpa"
    }
  ],
  "word": "symmetric group"
}