{
  "aliases": [
    "invariant-subgroup"
  ],
  "backlinks": [
    {
      "field": "about",
      "target": "0C9ZKYSPYR"
    },
    {
      "field": "about",
      "target": "0V547YQRMV"
    },
    {
      "field": "about",
      "target": "21JJ523V95"
    },
    {
      "field": "specializes",
      "target": "0GETX79CJN"
    },
    {
      "field": "specializes",
      "target": "0KABPMRHM2"
    },
    {
      "field": "defines",
      "target": "0W77CVBCHQ"
    },
    {
      "field": "uses",
      "target": "21JJ523V95"
    },
    {
      "field": "uses",
      "target": "2JABC6VSE1"
    },
    {
      "field": "uses",
      "target": "2XCJ8NNMXP"
    },
    {
      "field": "uses",
      "target": "383CHJH46R"
    },
    {
      "field": "uses",
      "target": "464TFVZ9JA"
    },
    {
      "field": "uses",
      "target": "64K1A69C80"
    },
    {
      "field": "uses",
      "target": "7Q3X4FG7A5"
    },
    {
      "field": "uses",
      "target": "7TP5M906HB"
    },
    {
      "field": "uses",
      "target": "8YYJBVP68F"
    },
    {
      "field": "uses",
      "target": "AADNYSB6TC"
    },
    {
      "field": "uses",
      "target": "ABKND96G8P"
    },
    {
      "field": "uses",
      "target": "BA2S40MM0Y"
    },
    {
      "field": "uses",
      "target": "DA515YH1J0"
    },
    {
      "field": "uses",
      "target": "DQCW86BXEP"
    },
    {
      "field": "uses",
      "target": "FESTJ0K9TX"
    },
    {
      "field": "uses",
      "target": "FQZJKY2G5Q"
    },
    {
      "field": "uses",
      "target": "MTWNAJMH1D"
    },
    {
      "field": "uses",
      "target": "MZ6XDATQKR"
    },
    {
      "field": "uses",
      "target": "QMYZ798EAR"
    },
    {
      "field": "uses",
      "target": "S17DY98VF2"
    },
    {
      "field": "uses",
      "target": "S31M1ZYJRK"
    },
    {
      "field": "uses",
      "target": "SAH4PD2J9T"
    },
    {
      "field": "uses",
      "target": "TACX13XZST"
    },
    {
      "field": "uses",
      "target": "VC3QNG6TKR"
    },
    {
      "field": "uses",
      "target": "VK7402274F"
    },
    {
      "field": "uses",
      "target": "XJF5V9WHKZ"
    },
    {
      "field": "uses",
      "target": "XK7H3YXBQT"
    },
    {
      "field": "uses",
      "target": "XT6EEXPD4P"
    },
    {
      "field": "uses",
      "target": "YE87R5CDJY"
    },
    {
      "field": "uses",
      "target": "Z4WVANZPK4"
    },
    {
      "field": "instance_of",
      "target": "556HZEYCQF"
    },
    {
      "field": "instance_of",
      "target": "8WJPSS7TE9"
    },
    {
      "field": "instance_of",
      "target": "T4PCQ68C5K"
    },
    {
      "field": "not_instance_of",
      "target": "XD0WBC1MWB"
    }
  ],
  "body": "\n## Summary\n\nA normal subgroup of a group is a subgroup that is equal to each of its conjugates.\nThe normal subgroups are exactly the subgroups that give quotient groups, and exactly the kernels of homomorphisms.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "invariant-subgroup"
    ],
    "inventory": [
      "F3D99PH13A"
    ],
    "kind": "concept",
    "msc": [
      "20A05"
    ],
    "name": "Normal subgroup",
    "same_as": {
      "wikidata": "Q743179",
      "wikipedia": "Normal subgroup"
    },
    "sources": [
      {
        "locator": "Definitions",
        "url": "https://en.wikipedia.org/wiki/Normal_subgroup"
      }
    ],
    "specializes": [
      "0X1JXT47GA"
    ],
    "tag": "0CB0DX5BVV"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0CB0DX5BVV/",
  "links": [
    {
      "field": "specializes",
      "target": "0X1JXT47GA"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0CB0DX5BVV.md",
  "msc": [
    "20A05"
  ],
  "name": "Normal subgroup",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0CB/0CB0DX5BVV.md",
  "status": null,
  "tag": "0CB0DX5BVV",
  "uri": "m2://0CB0DX5BVV",
  "url": "https://tamnd.github.io/math2/wiki/normal-subgroup/",
  "writing": {
    "tag": "0CB0DX5BVV",
    "kind": "concept",
    "level": "W2",
    "next": [
      {
        "what": "section Motivation",
        "note": "the question that the notion answers",
        "have": 0,
        "want": 1
      },
      {
        "what": "section History",
        "note": "who introduced the notion and when",
        "have": 0,
        "want": 1
      },
      {
        "what": "explanations for the audience",
        "have": 0,
        "want": 3
      },
      {
        "what": "a person confirmed each agent-written section",
        "note": "rule P04",
        "have": 0,
        "want": 1
      }
    ]
  }
}
