{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0JWZX6FKSH"
    },
    {
      "field": "about",
      "target": "2XCJ8NNMXP"
    },
    {
      "field": "about",
      "target": "FESTJ0K9TX"
    },
    {
      "field": "about",
      "target": "H1BSG0J5G1"
    },
    {
      "field": "about",
      "target": "WQQTFRZFBD"
    },
    {
      "field": "uses",
      "target": "2XCJ8NNMXP"
    },
    {
      "field": "uses",
      "target": "5M0HYY3RYV"
    },
    {
      "field": "uses",
      "target": "7Q3X4FG7A5"
    },
    {
      "field": "uses",
      "target": "E09VVB7BJQ"
    },
    {
      "field": "uses",
      "target": "FESTJ0K9TX"
    },
    {
      "field": "uses",
      "target": "GJBAX2R2PG"
    },
    {
      "field": "uses",
      "target": "H1BSG0J5G1"
    },
    {
      "field": "uses",
      "target": "VZ1G9CYQSK"
    },
    {
      "field": "uses",
      "target": "WQQTFRZFBD"
    }
  ],
  "body": "\n## Summary\n\nLet $G$ be a finite group, let $p$ be a prime number, and let $p^n$ be the largest power of $p$ that divides $|G|$.\nA Sylow $p$-subgroup of $G$ is a subgroup of order $p^n$.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "20D20"
    ],
    "name": "Sylow p-subgroup",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Sylow_theorems"
      }
    ],
    "specializes": [
      "0X1JXT47GA"
    ],
    "tag": "0053CQE9Y2"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0053CQE9Y2/",
  "links": [
    {
      "field": "specializes",
      "target": "0X1JXT47GA"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0053CQE9Y2.md",
  "msc": [
    "20D20"
  ],
  "name": "Sylow p-subgroup",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/005/0053CQE9Y2.md",
  "status": null,
  "tag": "0053CQE9Y2",
  "uri": "m2://0053CQE9Y2",
  "url": "https://tamnd.github.io/math2/wiki/sylow-p-subgroup/",
  "writing": {
    "tag": "0053CQE9Y2",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}