"torsion subgroup" meaning in All languages combined

{
  "forms": [
    {
      "form": "torsion subgroups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "torsion subgroup (plural torsion subgroups)",
      "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": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2006 July 7, Joseph H. Silverman, An Introduction to the Theory of Elliptic Curves",
          "text": "A standard theorem about finitely generated abelian groups tells us that E(#x5C;mathbb#x7B;Q#x7D;) looks like\nx5C;qquadE(#x5C;mathbb#x7B;Q#x7D;)#x5C;cong(#x5C;mbox#x7B;FiniteGroup#x7D;)#x5C;times#x5C;underbrace#x7B;#x5C;mathbb#x7B;Z#x7D;#x5C;times#x5C;mathbb#x7B;Z#x7D;#x5C;times...#x5C;times#x5C;mathbb#x7B;Z_(r mbox copies)\nqquad E(ℚ)≅E(ℚ)_(mbox tors)×⏟ℤ×ℤ×...×ℤ_(r mbox copies)\nThe finite subgroup E(ℚ)_(mbox tors) is called the\nqquad color red mbox TorsionSubgroupofE(ℚ).}}",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Subgroup of an abelian group whose generators have finite order."
      ],
      "id": "en-torsion_subgroup-en-noun-CbzsQXOI",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "abelian group",
          "abelian group"
        ],
        [
          "generator",
          "generator"
        ],
        [
          "order",
          "order#English-groupth"
        ]
      ],
      "raw_glosses": [
        "(algebra) Subgroup of an abelian group whose generators have finite order."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "torsion subgroup"
      ]
    }
  ],
  "word": "torsion subgroup"
}

{
  "forms": [
    {
      "form": "torsion subgroups",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "torsion subgroup (plural torsion subgroups)",
      "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",
        "en:Algebra"
      ],
      "examples": [
        {
          "ref": "2006 July 7, Joseph H. Silverman, An Introduction to the Theory of Elliptic Curves",
          "text": "A standard theorem about finitely generated abelian groups tells us that E(#x5C;mathbb#x7B;Q#x7D;) looks like\nx5C;qquadE(#x5C;mathbb#x7B;Q#x7D;)#x5C;cong(#x5C;mbox#x7B;FiniteGroup#x7D;)#x5C;times#x5C;underbrace#x7B;#x5C;mathbb#x7B;Z#x7D;#x5C;times#x5C;mathbb#x7B;Z#x7D;#x5C;times...#x5C;times#x5C;mathbb#x7B;Z_(r mbox copies)\nqquad E(ℚ)≅E(ℚ)_(mbox tors)×⏟ℤ×ℤ×...×ℤ_(r mbox copies)\nThe finite subgroup E(ℚ)_(mbox tors) is called the\nqquad color red mbox TorsionSubgroupofE(ℚ).}}",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Subgroup of an abelian group whose generators have finite order."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "abelian group",
          "abelian group"
        ],
        [
          "generator",
          "generator"
        ],
        [
          "order",
          "order#English-groupth"
        ]
      ],
      "raw_glosses": [
        "(algebra) Subgroup of an abelian group whose generators have finite order."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "torsion subgroup"
      ]
    }
  ],
  "word": "torsion subgroup"
}