{
  "aliases": [
    "relatively-hyperbolic"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, **relatively hyperbolic groups** form an important class of groups of interest for geometric group theory. The main purpose in their study is to extend the theory of Gromov-hyperbolic groups to groups $G$ that may be regarded as hyperbolic assemblies of subgroups $H_i$, called peripheral subgroups, in a way that enables \"hyperbolic reduction\" of problems for $G$ to problems for the $H_i$s.\n",
  "commit": "a799a9852bcfeae9dc83faa3bef60208bb53686b",
  "front": {
    "aliases": [
      "relatively-hyperbolic"
    ],
    "inventory": [
      "MEBY4802PP"
    ],
    "kind": "concept",
    "name": "Relatively hyperbolic group",
    "same_as": {
      "wikidata": "Q7310818",
      "wikipedia": "Relatively hyperbolic group"
    },
    "sources": [
      {
        "locator": "Relatively hyperbolic group",
        "mention": "wikipedia://en/21993809",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:21993809@r1305298879"
      }
    ],
    "tag": "E9VNR66B01"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/E9VNR66B01/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/E9VNR66B01.md",
  "msc": null,
  "name": "Relatively hyperbolic group",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/E9V/E9VNR66B01.md",
  "status": null,
  "tag": "E9VNR66B01",
  "uri": "m2://E9VNR66B01",
  "url": "https://math2.tamnd.com/wiki/relatively-hyperbolic-group/",
  "writing": {
    "tag": "E9VNR66B01",
    "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
      }
    ]
  }
}