"Margulis lemma" meaning in English

{
  "etymology_text": "Named after Grigory Margulis.",
  "forms": [
    {
      "form": "the Margulis lemma",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Margulis lemma",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Differential geometry",
          "orig": "en:Differential geometry",
          "parents": [
            "Geometry",
            "Mathematical analysis",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (the Margulis constant), the structure of the orbits of such a group cannot be too complicated. More precisely, within this radius around a point all points in its orbit are in fact in the orbit of a nilpotent subgroup (in fact a bounded finite number of such)."
      ],
      "id": "en-Margulis_lemma-en-name-FMr~8rA0",
      "links": [
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "result",
          "result"
        ],
        [
          "discrete",
          "discrete"
        ],
        [
          "subgroup",
          "subgroup"
        ],
        [
          "isometries",
          "isometry"
        ],
        [
          "Riemannian manifold",
          "Riemannian manifold"
        ],
        [
          "radius",
          "radius"
        ],
        [
          "Margulis constant",
          "Margulis constant"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "orbit",
          "orbit"
        ],
        [
          "point",
          "point"
        ],
        [
          "nilpotent",
          "nilpotent"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (the Margulis constant), the structure of the orbits of such a group cannot be too complicated. More precisely, within this radius around a point all points in its orbit are in fact in the orbit of a nilpotent subgroup (in fact a bounded finite number of such)."
      ],
      "wikipedia": [
        "Grigory Margulis"
      ]
    }
  ],
  "word": "Margulis lemma"
}

{
  "etymology_text": "Named after Grigory Margulis.",
  "forms": [
    {
      "form": "the Margulis lemma",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Margulis lemma",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Differential geometry"
      ],
      "glosses": [
        "A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (the Margulis constant), the structure of the orbits of such a group cannot be too complicated. More precisely, within this radius around a point all points in its orbit are in fact in the orbit of a nilpotent subgroup (in fact a bounded finite number of such)."
      ],
      "links": [
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "result",
          "result"
        ],
        [
          "discrete",
          "discrete"
        ],
        [
          "subgroup",
          "subgroup"
        ],
        [
          "isometries",
          "isometry"
        ],
        [
          "Riemannian manifold",
          "Riemannian manifold"
        ],
        [
          "radius",
          "radius"
        ],
        [
          "Margulis constant",
          "Margulis constant"
        ],
        [
          "structure",
          "structure"
        ],
        [
          "orbit",
          "orbit"
        ],
        [
          "point",
          "point"
        ],
        [
          "nilpotent",
          "nilpotent"
        ]
      ],
      "qualifier": "differential geometry",
      "raw_glosses": [
        "(differential geometry) A result about discrete subgroups of isometries of a non-positively curved Riemannian manifold, stating roughly that, within a fixed radius (the Margulis constant), the structure of the orbits of such a group cannot be too complicated. More precisely, within this radius around a point all points in its orbit are in fact in the orbit of a nilpotent subgroup (in fact a bounded finite number of such)."
      ],
      "wikipedia": [
        "Grigory Margulis"
      ]
    }
  ],
  "word": "Margulis lemma"
}