"Margulis lemma" meaning in English

{
  "etymology_text": "Named after Grigory Margulis.",
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  "lang_code": "en",
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      "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)."
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          "isometries",
          "isometry"
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        [
          "Riemannian manifold",
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        [
          "radius",
          "radius"
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        [
          "Margulis constant",
          "Margulis constant"
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          "structure"
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          "point",
          "point"
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          "nilpotent",
          "nilpotent"
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      ],
      "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"
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  "word": "Margulis lemma"
}

{
  "etymology_text": "Named after Grigory Margulis.",
  "forms": [
    {
      "form": "the Margulis lemma",
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        "canonical"
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        "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)."
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          "radius",
          "radius"
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          "Margulis constant"
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          "structure",
          "structure"
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          "orbit",
          "orbit"
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          "point",
          "point"
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      "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)."
      ],
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        "Grigory Margulis"
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    }
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}