"algebraic group" meaning in All languages combined

{
  "forms": [
    {
      "form": "algebraic groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "algebraic group (plural algebraic groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "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": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "linear algebraic group"
        }
      ],
      "examples": [
        {
          "ref": "1998, Martin W. Liebeck, “Introduction to the subgroup structure of algebraic groups”, in Roger William Carter, Meinolf Geck, H. K. Moffatt, editors, Representations of Reductive Groups, Cambridge University Press, page 129:",
          "text": "The purpose of this article is to discuss various results concerning the subgroups of simple algebraic groups G and of the corresponding finite groups of Lie type G^F (where F is a Frobenius morphism).",
          "type": "quote"
        },
        {
          "ref": "1998, Roe Goodman, Nolan R. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press, page 464:",
          "text": "We begin by showing how to make the quotient of an affine algebraic group by a normal algebraic subgroup into an affine algebraic group, and we determine the structure of commutative affine algebraic groups.",
          "type": "quote"
        },
        {
          "text": "2011, Teresa Crespo, Zbigniew Hajto, Algebraic Groups and Differential Galois Theory, American Mathematical Society, page 75,\nWe point out that some properties of an algebraic group are more easily read in its Lie algebra. An important property of an algebraic group is its solvability."
        }
      ],
      "glosses": [
        "A group that is an algebraic variety."
      ],
      "id": "en-algebraic_group-en-noun-5VmPxMnr",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "group",
          "group"
        ],
        [
          "algebraic variety",
          "algebraic variety"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A group that is an algebraic variety."
      ],
      "synonyms": [
        {
          "sense": "group that is an algebraic variety",
          "word": "group variety"
        }
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "algebraic group"
      ]
    }
  ],
  "word": "algebraic group"
}

{
  "derived": [
    {
      "word": "linear algebraic group"
    }
  ],
  "forms": [
    {
      "form": "algebraic groups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "algebraic group (plural algebraic groups)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Algebraic geometry"
      ],
      "examples": [
        {
          "ref": "1998, Martin W. Liebeck, “Introduction to the subgroup structure of algebraic groups”, in Roger William Carter, Meinolf Geck, H. K. Moffatt, editors, Representations of Reductive Groups, Cambridge University Press, page 129:",
          "text": "The purpose of this article is to discuss various results concerning the subgroups of simple algebraic groups G and of the corresponding finite groups of Lie type G^F (where F is a Frobenius morphism).",
          "type": "quote"
        },
        {
          "ref": "1998, Roe Goodman, Nolan R. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press, page 464:",
          "text": "We begin by showing how to make the quotient of an affine algebraic group by a normal algebraic subgroup into an affine algebraic group, and we determine the structure of commutative affine algebraic groups.",
          "type": "quote"
        },
        {
          "text": "2011, Teresa Crespo, Zbigniew Hajto, Algebraic Groups and Differential Galois Theory, American Mathematical Society, page 75,\nWe point out that some properties of an algebraic group are more easily read in its Lie algebra. An important property of an algebraic group is its solvability."
        }
      ],
      "glosses": [
        "A group that is an algebraic variety."
      ],
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "group",
          "group"
        ],
        [
          "algebraic variety",
          "algebraic variety"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) A group that is an algebraic variety."
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "algebraic group"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "group that is an algebraic variety",
      "word": "group variety"
    }
  ],
  "word": "algebraic group"
}