{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0RG9SPQSWM"
    }
  ],
  "body": "\n## Summary\n\nThe subgroup generated by a subset of a group is the smallest subgroup that contains the subset.\nIts elements are the finite products of elements of the subset and their inverses.\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "kind": "concept",
    "msc": [
      "20A05"
    ],
    "name": "Subgroup generated by a subset",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Generating_set_of_a_group"
      }
    ],
    "tag": "0RP7VWQ0YN"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0RP7VWQ0YN/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0RP7VWQ0YN.md",
  "msc": [
    "20A05"
  ],
  "name": "Subgroup generated by a subset",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0RP/0RP7VWQ0YN.md",
  "status": null,
  "tag": "0RP7VWQ0YN",
  "uri": "m2://0RP7VWQ0YN",
  "url": "https://math2.tamnd.com/wiki/subgroup-generated-by-a-subset/",
  "writing": {
    "tag": "0RP7VWQ0YN",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}