{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0HY15D6WTX"
    },
    {
      "field": "about",
      "target": "4AF7AF7690"
    },
    {
      "field": "about",
      "target": "GWZN3EKEWD"
    },
    {
      "field": "about",
      "target": "NTK1TVA50A"
    },
    {
      "field": "about",
      "target": "P7TZ694FCM"
    },
    {
      "field": "about",
      "target": "XWEMJ7T2XV"
    },
    {
      "field": "about",
      "target": "YB8V6TQDYE"
    },
    {
      "field": "uses",
      "target": "4AF7AF7690"
    },
    {
      "field": "uses",
      "target": "8MRPZ4Q4NM"
    },
    {
      "field": "uses",
      "target": "BZHGKN6Q3K"
    },
    {
      "field": "uses",
      "target": "E3ECET66DQ"
    },
    {
      "field": "uses",
      "target": "FQZJKY2G5Q"
    },
    {
      "field": "uses",
      "target": "GWZN3EKEWD"
    },
    {
      "field": "uses",
      "target": "JNB1VM75XP"
    },
    {
      "field": "uses",
      "target": "JT4F3SKPCP"
    },
    {
      "field": "uses",
      "target": "KHTCR3VFST"
    },
    {
      "field": "uses",
      "target": "MXRCPAH09H"
    },
    {
      "field": "uses",
      "target": "NTK1TVA50A"
    },
    {
      "field": "uses",
      "target": "P7TZ694FCM"
    },
    {
      "field": "uses",
      "target": "QYXGVES1XM"
    },
    {
      "field": "uses",
      "target": "RSBFHHPTWX"
    },
    {
      "field": "uses",
      "target": "XWEMJ7T2XV"
    },
    {
      "field": "uses",
      "target": "YB8V6TQDYE"
    },
    {
      "field": "specializes",
      "target": "TJKANTKASZ"
    }
  ],
  "body": "\n## Summary\n\nA finitely generated group is a group that a finite subset generates.\nAll finite groups and the group of integers are finitely generated.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "X45XA5XYK1"
    ],
    "kind": "concept",
    "msc": [
      "20F05"
    ],
    "name": "Finitely generated group",
    "same_as": {
      "wikidata": "Q21083858",
      "wikipedia": "Finitely generated group"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Finitely_generated_group"
      }
    ],
    "specializes": [
      "G5S1M9"
    ],
    "tag": "082DWWXMRJ"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/082DWWXMRJ/",
  "links": [
    {
      "field": "specializes",
      "target": "G5S1M9"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/082DWWXMRJ.md",
  "msc": [
    "20F05"
  ],
  "name": "Finitely generated group",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/082/082DWWXMRJ.md",
  "status": null,
  "tag": "082DWWXMRJ",
  "uri": "m2://082DWWXMRJ",
  "url": "https://tamnd.github.io/math2/wiki/finitely-generated-group/",
  "writing": {
    "tag": "082DWWXMRJ",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "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
      }
    ]
  }
}