{
  "aliases": [
    "period-of-an-element"
  ],
  "backlinks": [
    {
      "field": "about",
      "target": "08V7JHS3QZ"
    },
    {
      "field": "defines",
      "target": "0JPYSD5E0B"
    },
    {
      "field": "uses",
      "target": "2XCJ8NNMXP"
    },
    {
      "field": "uses",
      "target": "8T34EC16NH"
    },
    {
      "field": "uses",
      "target": "ETJ4WRXC41"
    },
    {
      "field": "uses",
      "target": "G38B7E4ESW"
    },
    {
      "field": "uses",
      "target": "GAD8ZE5MPV"
    },
    {
      "field": "uses",
      "target": "K5CQM8MYYG"
    },
    {
      "field": "uses",
      "target": "M5FDV1TMBG"
    },
    {
      "field": "uses",
      "target": "VQ4SSKS53D"
    },
    {
      "field": "uses",
      "target": "XWEMJ7T2XV"
    },
    {
      "field": "instance_of",
      "target": "77N4TVRM15"
    },
    {
      "field": "instance_of",
      "target": "Y20PEX049W"
    }
  ],
  "body": "\n## Summary\n\nThe order of an element of a group is the smallest positive integer $n$ such that the $n$th power of the element is the identity.\nWhen no such $n$ exists, the element has infinite order.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "aliases": [
      "period-of-an-element"
    ],
    "inventory": [
      "2WR87G5VKX"
    ],
    "kind": "concept",
    "msc": [
      "20A05"
    ],
    "name": "Order of an element",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Order_(group_theory)"
      }
    ],
    "tag": "0WE2NHZJ7B"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0WE2NHZJ7B/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/0WE2NHZJ7B.md",
  "msc": [
    "20A05"
  ],
  "name": "Order of an element",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0WE/0WE2NHZJ7B.md",
  "status": null,
  "tag": "0WE2NHZJ7B",
  "uri": "m2://0WE2NHZJ7B",
  "url": "https://tamnd.github.io/math2/wiki/order-of-an-element/",
  "writing": {
    "tag": "0WE2NHZJ7B",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}