"Möbius group" meaning in All languages combined

{
  "etymology_text": "Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.",
  "forms": [
    {
      "form": "Möbius groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Möbius group (plural Möbius groups)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "_dis1": "52 48",
      "word": "Lie group"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "_dis1": "52 48",
      "word": "Möbius transformation"
    }
  ],
  "pos": "noun",
  "related": [
    {
      "_dis1": "52 48",
      "word": "Möbius strip"
    },
    {
      "_dis1": "52 48",
      "word": "Möbius transformation"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
          "parents": [
            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "66 34",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "68 32",
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "66 34",
          "kind": "other",
          "name": "English entries with topic categories using raw markup",
          "parents": [
            "Entries with topic categories using raw markup",
            "Entry maintenance"
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          "source": "w+disamb"
        },
        {
          "_dis": "68 32",
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "75 25",
          "kind": "other",
          "langcode": "en",
          "name": "Non-Euclidean geometry",
          "orig": "en:Non-Euclidean geometry",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
      "id": "en-Möbius_group-en-noun-J0is7NYn",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "projective general linear group",
          "projective general linear group"
        ],
        [
          "Möbius transformations",
          "Möbius transformations"
        ],
        [
          "Riemann sphere",
          "Riemann sphere"
        ]
      ],
      "raw_glosses": [
        "(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "96 4",
          "code": "nl",
          "lang": "Dutch",
          "sense": "PGL(2,C)",
          "tags": [
            "feminine",
            "masculine"
          ],
          "word": "Möbius-groep"
        },
        {
          "_dis1": "96 4",
          "code": "es",
          "lang": "Spanish",
          "sense": "PGL(2,C)",
          "tags": [
            "masculine"
          ],
          "word": "grupo de Möbius"
        }
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Group theory",
          "orig": "en:Group theory",
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            "Algebra",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
      "id": "en-Möbius_group-en-noun-ohRFK8Nm",
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group"
        ],
        [
          "hypersphere",
          "hypersphere"
        ],
        [
          "invariant",
          "invariant"
        ]
      ],
      "raw_glosses": [
        "(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "_dis1": "52 48",
      "word": "Moebius group"
    },
    {
      "_dis1": "52 48",
      "word": "Mobius group"
    }
  ],
  "wikipedia": [
    "Möbius group"
  ],
  "word": "Möbius group"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English entries with language name categories using raw markup",
    "English entries with topic categories using raw markup",
    "English eponyms",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "English terms spelled with Ö",
    "English terms spelled with ◌̈",
    "English terms with non-redundant non-automated sortkeys",
    "en:Non-Euclidean geometry"
  ],
  "etymology_text": "Eponymous for August Ferdinand Möbius (1790–1868), a German mathematician and theoretical astronomer.",
  "forms": [
    {
      "form": "Möbius groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Möbius group (plural Möbius groups)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "Lie group"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "word": "Möbius transformation"
    }
  ],
  "pos": "noun",
  "related": [
    {
      "word": "Möbius strip"
    },
    {
      "word": "Möbius transformation"
    }
  ],
  "senses": [
    {
      "categories": [
        "en:Group theory"
      ],
      "glosses": [
        "The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "projective general linear group",
          "projective general linear group"
        ],
        [
          "Möbius transformations",
          "Möbius transformations"
        ],
        [
          "Riemann sphere",
          "Riemann sphere"
        ]
      ],
      "raw_glosses": [
        "(group theory) The projective general linear group mathbf PGL(2,ℂ): the group of Möbius transformations on the Riemann sphere."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Group theory"
      ],
      "glosses": [
        "For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
      "links": [
        [
          "group theory",
          "group theory"
        ],
        [
          "group",
          "group"
        ],
        [
          "hypersphere",
          "hypersphere"
        ],
        [
          "invariant",
          "invariant"
        ]
      ],
      "raw_glosses": [
        "(group theory) For a given dimension n, the group of projective transformations leaving a particular hypersphere invariant."
      ],
      "topics": [
        "group-theory",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "Moebius group"
    },
    {
      "word": "Mobius group"
    }
  ],
  "translations": [
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "PGL(2,C)",
      "tags": [
        "feminine",
        "masculine"
      ],
      "word": "Möbius-groep"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "PGL(2,C)",
      "tags": [
        "masculine"
      ],
      "word": "grupo de Möbius"
    }
  ],
  "wikipedia": [
    "Möbius group"
  ],
  "word": "Möbius group"
}