{
  "aliases": null,
  "backlinks": [
    {
      "field": "specializes",
      "target": "08ABT85339"
    },
    {
      "field": "defines",
      "target": "0RG9SPQSWM"
    },
    {
      "field": "uses",
      "target": "61F4HEY84K"
    },
    {
      "field": "uses",
      "target": "7Q3X4FG7A5"
    },
    {
      "field": "uses",
      "target": "E3ECET66DQ"
    },
    {
      "field": "uses",
      "target": "G0JDQQRTGV"
    },
    {
      "field": "uses",
      "target": "GMPJ88PAQE"
    },
    {
      "field": "uses",
      "target": "H1BSG0J5G1"
    },
    {
      "field": "uses",
      "target": "JT4F3SKPCP"
    }
  ],
  "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": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "inventory": [
      "120ECZQBX2"
    ],
    "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"
      }
    ],
    "specializes": [
      "0X1JXT47GA"
    ],
    "tag": "0RP7VWQ0YN"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0RP7VWQ0YN/",
  "links": [
    {
      "field": "specializes",
      "target": "0X1JXT47GA"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/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://tamnd.github.io/math2/wiki/subgroup-generated-by-a-subset/",
  "writing": {
    "tag": "0RP7VWQ0YN",
    "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
      }
    ]
  }
}
