{
  "aliases": [
    "zero-group"
  ],
  "backlinks": null,
  "body": "\n## Example\n\nThe trivial group is the [[group|G5S1M9]] $\\{e\\}$ with one element $e$ and the operation $e \\cdot e = e$.\nThe element $e$ is the identity element, and it is its own inverse.\nEach group with exactly one element is isomorphic to this group.\n\n## Remarks\n\nEach group $G$ contains a trivial subgroup $\\{e\\}$, where $e$ is the identity of $G$.\nIn additive notation the trivial group is written $0$ or $\\{0\\}$.\nThe trivial group is [[abelian|082GHNPJ53]], and its order is $1$.\n\n## Explanations\n\n### L1 human\n\nThe trivial group is the smallest possible group: it has only the identity element.\nIt satisfies all the group axioms in a simple way.\nIt is often an edge case in theorems, for example when a theorem asks for a group that is not trivial.\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "aliases": [
      "zero-group"
    ],
    "instance_of": [
      "G5S1M9"
    ],
    "kind": "example",
    "msc": [
      "20A05"
    ],
    "name": "Trivial group",
    "same_as": {
      "wikidata": "Q568687",
      "wikipedia": "Trivial group"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Trivial_group"
      }
    ],
    "tag": "0BNPC9850Y"
  },
  "kind": "example",
  "link": "https://math2.tamnd.com/node/0BNPC9850Y/",
  "links": [
    {
      "field": "instance_of",
      "target": "G5S1M9"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0BNPC9850Y.md",
  "msc": [
    "20A05"
  ],
  "name": "Trivial group",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0BN/0BNPC9850Y.md",
  "status": null,
  "tag": "0BNPC9850Y",
  "uri": "m2://0BNPC9850Y",
  "url": "https://math2.tamnd.com/wiki/trivial-group/",
  "writing": {
    "tag": "0BNPC9850Y",
    "kind": "example",
    "level": "W2",
    "next": [
      {
        "what": "a person confirmed each agent-written section",
        "note": "rule P04",
        "have": 0,
        "want": 1
      }
    ]
  }
}