{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, specifically group theory, a **descendant tree** is a hierarchical structure that visualizes parent-descendant relations between isomorphism classes of finite groups of prime power order $p^n$, for a fixed prime number $p$ and varying integer exponents $n\\ge 0$. Such groups are briefly called *finite* [[*p-groups*|06QYRTX9KQ]]. The *vertices* of a [[descendant tree|062D9KXJB1]] are isomorphism classes of finite *p*-groups.\n",
  "commit": "a799a9852bcfeae9dc83faa3bef60208bb53686b",
  "front": {
    "inventory": [
      "C7KVWD061H"
    ],
    "kind": "concept",
    "name": "Descendant tree (group theory)",
    "same_as": {
      "wikidata": "Q113884406",
      "wikipedia": "Descendant tree (group theory)"
    },
    "sources": [
      {
        "locator": "Descendant tree (group theory)",
        "mention": "wikipedia://en/42823620",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:42823620@r1324320219"
      }
    ],
    "tag": "71GNXXRD5V"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/71GNXXRD5V/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/71GNXXRD5V.md",
  "msc": null,
  "name": "Descendant tree (group theory)",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/71G/71GNXXRD5V.md",
  "status": null,
  "tag": "71GNXXRD5V",
  "uri": "m2://71GNXXRD5V",
  "url": "https://math2.tamnd.com/wiki/descendant-tree-group-theory/",
  "writing": {
    "tag": "71GNXXRD5V",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "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
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}