{
  "aliases": [
    "p-group"
  ],
  "backlinks": [
    {
      "field": "defines",
      "target": "06DAH3VS6M"
    },
    {
      "field": "uses",
      "target": "2JABC6VSE1"
    },
    {
      "field": "uses",
      "target": "BRHQQTZB9K"
    },
    {
      "field": "uses",
      "target": "FESTJ0K9TX"
    },
    {
      "field": "uses",
      "target": "G0JDQQRTGV"
    },
    {
      "field": "uses",
      "target": "NB057FEAAE"
    },
    {
      "field": "uses",
      "target": "RC5A5T7YY2"
    },
    {
      "field": "uses",
      "target": "V8JVWE87TE"
    },
    {
      "field": "specializes",
      "target": "7YE4TAG5GE"
    }
  ],
  "body": "\n## Summary\n\nFor a prime number $p$, a $p$-group is a group in which the order of each element is a power of $p$.\nA finite group is a $p$-group if and only if its order is a power of $p$.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "p-group"
    ],
    "kind": "concept",
    "msc": [
      "20D15"
    ],
    "name": "P-group",
    "same_as": {
      "wikidata": "Q286972",
      "wikipedia": "P-group"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/P-group"
      }
    ],
    "specializes": [
      "G5S1M9"
    ],
    "tag": "06QYRTX9KQ"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/06QYRTX9KQ/",
  "links": [
    {
      "field": "specializes",
      "target": "G5S1M9"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/06QYRTX9KQ.md",
  "msc": [
    "20D15"
  ],
  "name": "P-group",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/06Q/06QYRTX9KQ.md",
  "status": null,
  "tag": "06QYRTX9KQ",
  "uri": "m2://06QYRTX9KQ",
  "url": "https://tamnd.github.io/math2/wiki/p-group/",
  "writing": {
    "tag": "06QYRTX9KQ",
    "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
      }
    ]
  }
}