{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, in the area of abstract algebra known as group theory, a **verbal subgroup** is a [[subgroup|0X1JXT47GA]] of a group that is [[generated|0MBV2VHMXA]] by all elements that can be formed by substituting group elements for variables in a given set of words. For example, given the word $x^2$, the corresponding verbal subgroup is the group generated by all squares.\n",
  "commit": "a799a9852bcfeae9dc83faa3bef60208bb53686b",
  "front": {
    "inventory": [
      "8BRYVJ85JK"
    ],
    "kind": "concept",
    "name": "Verbal subgroup",
    "same_as": {
      "wikidata": "Q7920943",
      "wikipedia": "Verbal subgroup"
    },
    "sources": [
      {
        "locator": "Verbal subgroup",
        "mention": "wikipedia://en/21674070",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:21674070@r1361555339"
      }
    ],
    "tag": "HRYZGA8V0K"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/HRYZGA8V0K/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/HRYZGA8V0K.md",
  "msc": null,
  "name": "Verbal subgroup",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/HRY/HRYZGA8V0K.md",
  "status": null,
  "tag": "HRYZGA8V0K",
  "uri": "m2://HRYZGA8V0K",
  "url": "https://math2.tamnd.com/wiki/verbal-subgroup/",
  "writing": {
    "tag": "HRYZGA8V0K",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}