group

algebraic set with an invertible, associative internal operation admitting a neutral element
rdfs:label
"group"@en
skos:altLabel
"algebraic group"@en
"group (algebra)"@en
"group (math)"@en
"mathematical group"@en
schema:description
"algebraic set with an invertible, associative internal operation admitting a neutral element"@en
schema:dateModified "2026-10-14T21:15:01+00:00"^^xsd:dateTime
schema:version 2557039180
wikibase:identifiers 33
wikibase:sitelinks 92
wikibase:statements 73
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wd:statement/Q83478-7fbd4305-4cf7-725e-4fd6-b469e58d60c5
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p:P2354 wd:statement/Q83478-aa8490ed-4e8b-62d2-6dbe-fba75ca5c066
p:P2534 wd:statement/Q83478-6874b528-404f-3b96-4867-ccd8935ee8f4
p:P2579 wd:statement/Q83478-634f5176-41f9-348f-975b-1d7d5db035eb
wd:statement/Q83478-7f41e656-4d3e-0b83-3108-e0a27996746b
wd:statement/Q83478-F5A5AF16-A303-40CB-B0B5-3BAADC21F20B
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wd:statement/Q83478-3F502F3B-70D7-4151-B8C8-ADE4389232EE
wd:statement/Q83478-a02285c4-44cd-eb27-4663-3a189b072d01
wd:statement/Q83478-c6dcd147-4591-ba2a-1748-c7e0e59f3d87
wd:statement/Q83478-def56bd7-4763-260e-5c84-fc33b9c76978
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wd:statement/q83478-92e37147-45e6-4c62-7e78-02d26204456e
p:P2812 wd:statement/Q83478-111ce4b3-4f40-3d50-77fc-d595b05e5822
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p:P3219 wd:statement/Q83478-D4907AAF-F983-4D39-9E04-DA69B0BC29A9
wd:statement/Q83478-D75F3556-58A1-4743-9874-41ECD6D63085
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p:P373 wd:statement/Q83478-BE39A261-79DC-4745-AC6A-C4C0C3390D12
p:P4215 wd:statement/Q83478-12a33b9d-422c-6af2-e601-801d41bf94b9
p:P4342 wd:statement/Q83478-0c68e8be-438d-2ff9-d403-571dca7ec369
p:P5008 wd:statement/Q83478-9C6900A9-22B7-40EB-BE0B-9A2B069EBFE4
p:P5019 wd:statement/Q83478-ea1e5865-479f-8dd9-bb14-2cfd2f275b10
p:P508 wd:statement/Q83478-e56f0acf-4f2e-268b-aacd-0bcde729f455
p:P527 wd:statement/Q83478-48f86f21-4524-f46c-bce7-0e71ad89caa6
wd:statement/Q83478-79461195-47c1-94fa-d133-a80b4fc7070a
wd:statement/Q83478-d5231d7e-4939-f80a-9951-6eb1c189dad5
wd:statement/Q83478-eb696a32-44ef-8302-e3cf-2694cab04069
p:P5555 wd:statement/Q83478-67fd09a7-44af-658b-0c8b-3fff45b667a3
p:P5844 wd:statement/Q83478-9c282bbf-4edb-1e52-5a7d-e1a38852cf43
p:P6058 wd:statement/Q83478-b49b7d96-427f-4551-25d6-f7822af32eb1
p:P6104 wd:statement/Q83478-A3271D8C-9CCB-4BDD-803E-51B201255C2E
p:P6366 wd:statement/Q83478-F04474E3-75C5-448B-875F-952C2F3AAA3E
p:P646 wd:statement/Q83478-BEC0DF11-6F2F-4A4D-A204-26AB9C6372CA
p:P6706 wd:statement/Q83478-6d3c8712-49db-a501-2947-85fb23fad939
p:P6900 wd:statement/Q83478-b3ff2eb6-4b78-6635-696a-d50c82c9f9c0
p:P691 wd:statement/Q83478-CC36AC47-0945-4DD8-A35D-2142589C0818
p:P7235 wd:statement/Q83478-16099dde-4b59-aa2b-c18c-d0c76c4b1bd5
wd:statement/Q83478-1bfeb44c-4c6b-1f64-0e71-2b0381ab1217
wd:statement/Q83478-4a67f9c1-43a4-e757-5ebc-bb0320bd25b8
wd:statement/Q83478-80596cc0-4f8d-70b7-6087-eb5417a4e44b
wd:statement/Q83478-b8444ad3-441c-2aa1-b2ea-566d23c39a96
wd:statement/Q83478-df4828fa-4678-4f85-fba4-547e454d4ac7
p:P7305 wd:statement/Q83478-4C56F9D7-F8EC-42ED-B0A6-F7BE957024CA
p:P7554 wd:statement/Q83478-c9da1046-491e-48ac-ec8b-c52e5ee3eb8f
p:P7666 wd:statement/Q83478-c160ee6e-40b7-8a47-70f5-612cf067578b
p:P7726 wd:statement/Q83478-b4e8c044-4cb0-7dd1-2b69-d056e3d811d6
p:P8408 wd:statement/Q83478-1C9C1E71-1053-404E-B3CA-C4BFBC98F315
p:P8417 wd:statement/Q83478-ec7945e6-4fea-2c29-edf9-793ea1737412
p:P8814 wd:statement/Q83478-388AF0B4-05C6-4CE5-A015-AB9D2B89E9AB
p:P8885 wd:statement/Q83478-9c591d4c-4067-0012-1a11-04d759e74735
p:P910 wd:statement/Q83478-DCAE9244-075A-4DBE-B8A7-78CFD61B28F0
p:direct-normalized/P227 <https://d-nb.info/gnd/4022379-6>
p:direct-normalized/P2581 <http://babelnet.org/rdf/s00041943n>
p:direct-normalized/P508 <http://purl.org/bncf/tid/5497>
p:direct-normalized/P6366 <https://makg.org/entity/93063749>
p:direct-normalized/P8408 <http://kbpedia.org/kko/rc/Group-Mathematics>
p:direct-normalized/P8814 <http://wordnet-rdf.princeton.edu/rdf/id/06026202-n>
wdt:P1036 "512.2"
wdt:P10556 "gruppi"
wdt:P12385 "algebra-associativa"
wdt:P12888 "df-grp"
wdt:P1296 "0157361"
wdt:P12987 "group"
wdt:P1343 Mathwords
wdt:P1417 "topic/group-mathematics"
wdt:P1424 Template:Group navbox
wdt:P14534 "Group"
wdt:P1552 Latin square property
associativity
identity element
inverse element
closure
wdt:P18 <http://commons.wikimedia.org/wiki/Special:FilePath/Rubiks%20revenge%20tilt.jpg>
wdt:P1889 group
wdt:P1963 group cardinality
wdt:P227 "4022379-6"
wdt:P2354 Examples of groups
wdt:P2534 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><mo stretchy="false">(</mo><mo stretchy="false">&#x22C5;</mo><mo stretchy="false">)</mo><mo stretchy="false">&#x003A;</mo><mi>G</mi><mo stretchy="false">&#x00D7;</mo><mi>G</mi><mo stretchy="false" accent="false">&#x2192;</mo><mi>G</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">&#x2200;</mi><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo stretchy="false">&#x2208;</mo><mi>G</mi><mo stretchy="false">&#x003A;</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">&#x22C5;</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">&#x22C5;</mo><mi>z</mi><mo stretchy="false">=</mo><mi>x</mi><mo stretchy="false">&#x22C5;</mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">&#x22C5;</mo><mi>z</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">&#x2203;</mi><mn>1</mn><mo stretchy="false">&#x2208;</mo><mi>G</mi><mi mathvariant="normal">&#x2200;</mi><mi>x</mi><mo stretchy="false">&#x2208;</mo><mi>G</mi><mo stretchy="false">&#x003A;</mo><mn>1</mn><mo stretchy="false">&#x22C5;</mo><mi>x</mi><mo stretchy="false">=</mo><mi>x</mi><mo stretchy="false">&#x22C5;</mo><mn>1</mn><mo stretchy="false">=</mo><mi>x</mi></mtd></mtr><mtr><mtd></mtd><mtd><mi mathvariant="normal">&#x2200;</mi><mi>x</mi><mo stretchy="false">&#x2208;</mo><mi>G</mi><mi mathvariant="normal">&#x2203;</mi><mi>y</mi><mo stretchy="false">&#x2208;</mo><mi>G</mi><mo stretchy="false">&#x003A;</mo><mi>x</mi><mo stretchy="false">&#x22C5;</mo><mi>y</mi><mo stretchy="false">=</mo><mi>y</mi><mo stretchy="false">&#x22C5;</mo><mi>x</mi><mo stretchy="false">=</mo><mn>1</mn></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P2579 abstract algebra
category theory
group theory
wdt:P2581 "00041943n"
wdt:P279 groupoid
algebraic structure
monoid
inverse semigroup
loop
epigroup
Moufang loop
group object
wdt:P2812 "Group"
wdt:P2888 <http://www.farzanegi.org/math/Group?lang=PA>
wdt:P31 mathematical concept
wdt:P3219 "groupes-mathematiques-generalites"
"groupes-mathematiques-vue-d-ensemble"
wdt:P3365 "gruppo"
wdt:P373 "Group theory"
wdt:P4215 "group"
wdt:P4342 "gruppe_-_matematikk"
wdt:P5008 Wikipedia:Vital articles/Level/4
wdt:P5019 "gruppe-mathematik"
wdt:P508 "5497"
wdt:P527 binary operation
identity element
set
inverse
wdt:P5555 <http://commons.wikimedia.org/wiki/Special:FilePath/Cayley%20graph%20Q8.svg>
wdt:P5844 "gruppo"
wdt:P6058 "divers/groupe/186120"
wdt:P6104 WikiProject Mathematics
wdt:P6366 "93063749"
wdt:P646 "/m/04xl4"
wdt:P6706 "gruppo+(algebra)"
wdt:P6900 "群(数学)"
wdt:P691 "ph180740"
wdt:P7235 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>G</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>x</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>z</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1</mn></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mo stretchy="false">&#x22C5;</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7305 "3908259"
wdt:P7554 "Group"
wdt:P7666 "grupe"
wdt:P7726 "Group"
wdt:P8408 "Group-Mathematics"
wdt:P8417 "Group"
wdt:P8814 "06026202-n"
wdt:P8885 "군(대수학)"
wdt:P910 wd:Q13324638
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