{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0JZY3R908H"
    }
  ],
  "body": "\n## Summary\n\nThe Galois group of a polynomial over a field is the Galois group of its splitting field.\nIt acts on the roots of the polynomial by permutations.\nThe [[definition of the Galois group of a polynomial|0JZY3R908H]] states it.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "kind": "concept",
    "msc": [
      "12F10"
    ],
    "name": "Galois group of a polynomial",
    "sources": [
      {
        "locator": "Galois group of a polynomial",
        "url": "https://en.wikipedia.org/wiki/Galois_group"
      }
    ],
    "tag": "0Q5NA8Y362"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0Q5NA8Y362/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0Q5NA8Y362.md",
  "msc": [
    "12F10"
  ],
  "name": "Galois group of a polynomial",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0Q5/0Q5NA8Y362.md",
  "status": null,
  "tag": "0Q5NA8Y362",
  "uri": "m2://0Q5NA8Y362",
  "url": "https://math2.tamnd.com/wiki/galois-group-of-a-polynomial/",
  "writing": {
    "tag": "0Q5NA8Y362",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}