"derived group" meaning in English

{
  "forms": [
    {
      "form": "derived groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "derived group (plural derived 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"
        },
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        },
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The subgroup of a specified group generated by the larger group's commutators."
      ],
      "id": "en-derived_group-en-noun-LfuBLgYg",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "subgroup",
          "subgroup"
        ],
        [
          "generate",
          "generate"
        ],
        [
          "commutator",
          "commutator"
        ]
      ],
      "raw_glosses": [
        "(algebra) The subgroup of a specified group generated by the larger group's commutators."
      ],
      "related": [
        {
          "word": "derived series"
        }
      ],
      "synonyms": [
        {
          "word": "commutator subgroup"
        },
        {
          "word": "derived subgroup"
        }
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "derived group"
}

{
  "forms": [
    {
      "form": "derived groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "derived group (plural derived groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "derived series"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
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        "en:Algebra"
      ],
      "glosses": [
        "The subgroup of a specified group generated by the larger group's commutators."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "subgroup",
          "subgroup"
        ],
        [
          "generate",
          "generate"
        ],
        [
          "commutator",
          "commutator"
        ]
      ],
      "raw_glosses": [
        "(algebra) The subgroup of a specified group generated by the larger group's commutators."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "commutator subgroup"
    },
    {
      "word": "derived subgroup"
    }
  ],
  "word": "derived group"
}