group (Q1253): Difference between revisions

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Property / image
 
Property / image: Rubiks revenge tilt.jpg / rank
 
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Property / subclass of
 
Property / subclass of: monoid / rank
 
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Property / subclass of
 
Property / subclass of: inverse semigroup / rank
 
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Property / subclass of
 
Property / subclass of: Moufang loop / rank
 
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Property / subclass of
 
Property / subclass of: groupoid / rank
 
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Property / subclass of
 
Property / subclass of: epigroup / rank
 
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Property / subclass of
 
Property / subclass of: algebraic structure / rank
 
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Property / subclass of
 
Property / subclass of: group object / rank
 
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Property / subclass of: group object / qualifier
 
Property / subclass of
 
Property / subclass of: loop / rank
 
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Property / Freebase ID
 
/m/04xl4
Property / Freebase ID: /m/04xl4 / rank
 
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Property / Freebase ID: /m/04xl4 / reference
 
stated in: Freebase Data Dumps
publication date: 28 October 2013
Timestamp+2013-10-28T00:00:00Z
Timezone+00:00
CalendarGregorian
Precision1 day
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Property / topic's main category
 
Property / topic's main category: Q2687 / rank
 
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Property / topic's main category: Q2687 / reference
 
Property / GND ID
 
4022379-6
Property / GND ID: 4022379-6 / rank
 
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Property / GND ID: 4022379-6 / reference
 
Property / Commons category
 
Group theory
Property / Commons category: Group theory / rank
 
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Property / Commons category: Group theory / reference
 
Property / MathWorld ID
 
Group
Property / MathWorld ID: Group / rank
 
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Property / Encyclopædia Britannica Online ID
 
topic/group-mathematics
Property / Encyclopædia Britannica Online ID: topic/group-mathematics / rank
 
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Property / Encyclopædia Britannica Online ID: topic/group-mathematics / qualifier
 
Property / BNCF Thesaurus ID
 
5497
Property / BNCF Thesaurus ID: 5497 / rank
 
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Property / has list
 
Property / has list: Examples of groups / rank
 
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Property / has characteristic
 
Property / has characteristic: closure / rank
 
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Property / has characteristic
 
Property / has characteristic: associativity / rank
 
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Property / has characteristic
 
Property / has characteristic: identity element / rank
 
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Property / has characteristic
 
Property / has characteristic: inverse element / rank
 
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Property / has characteristic
 
Property / has characteristic: Latin square property / rank
 
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Property / studied in
 
Property / studied in: group theory / rank
 
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Property / studied in
 
Property / studied in: category theory / rank
 
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Property / studied in
 
Property / studied in: abstract algebra / rank
 
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Property / defining formula
 

\begin{aligned}&(\cdot)\colon G\times G\to G\\&\forall x,y,z\in G\colon (x\cdot y)\cdot z=x\cdot(y\cdot z)\\&\exists1\in G\forall x\in G\colon 1\cdot x=x\cdot1=x\\&\forall x\in G\exists y\in G\colon x\cdot y=y\cdot x=1\end{aligned}
Property / defining formula: / rank
 
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Property / BabelNet ID
 
00041943n
Property / BabelNet ID: 00041943n / rank
 
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Property / BabelNet ID: 00041943n / reference
 
Property / properties for this type
 
Property / properties for this type: group cardinality / rank
 
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Property / Brockhaus Enzyklopädie online ID
 
gruppe-mathematik
Property / Brockhaus Enzyklopädie online ID: gruppe-mathematik / rank
 
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Property / Encyclopædia Universalis ID
 
groupes-mathematiques-generalites
Property / Encyclopædia Universalis ID: groupes-mathematiques-generalites / rank
 
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Property / Encyclopædia Universalis ID
 
groupes-mathematiques-vue-d-ensemble
Property / Encyclopædia Universalis ID: groupes-mathematiques-vue-d-ensemble / rank
 
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Property / has part(s)
 
Property / has part(s): set / rank
 
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Property / has part(s)
 
Property / has part(s): binary operation / rank
 
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Property / has part(s)
 
Property / has part(s): identity element / rank
 
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Property / has part(s)
 
Property / has part(s): inverse / rank
 
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Property / Microsoft Academic ID
 
93063749
Property / Microsoft Academic ID: 93063749 / rank
 
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Property / topic's main template
 
Property / topic's main template: Template:Group navbox / rank
 
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Property / topic's main template: Template:Group navbox / reference
 
Property / KBpedia ID
 
Group-Mathematics
Property / KBpedia ID: Group-Mathematics / rank
 
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Property / KBpedia ID: Group-Mathematics / reference
 
stated in: KBpedia
retrieved: 9 July 2020
Timestamp+2020-07-09T00:00:00Z
Timezone+00:00
CalendarGregorian
Precision1 day
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Property / different from
 
Property / different from: group / rank
 
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Property / PlanetMath ID
 
Group
Property / PlanetMath ID: Group / rank
 
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Property / Online PWN Encyclopedia ID
 
3908259
Property / Online PWN Encyclopedia ID: 3908259 / rank
 
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Property / Namuwiki ID
 
군(대수학)
Property / Namuwiki ID: 군(대수학) / rank
 
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Property / schematic
 
Property / schematic: Cayley graph Q8.svg / rank
 
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Property / Encyclopedia of Mathematics article ID
 
Group
Property / Encyclopedia of Mathematics article ID: Group / rank
 
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Property / nLab ID
 
group
Property / nLab ID: group / rank
 
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Property / Store norske leksikon ID
 
gruppe_-_matematikk
Property / Store norske leksikon ID: gruppe_-_matematikk / rank
 
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Property / WordNet 3.1 Synset ID
 
06026202-n
Property / WordNet 3.1 Synset ID: 06026202-n / rank
 
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Property / WordNet 3.1 Synset ID: 06026202-n / reference
 
Property / on focus list of Wikimedia project
 
Property / on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4 / rank
 
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Property / on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4 / qualifier
 
point in time: 31 October 2022
Timestamp+2022-10-31T00:00:00Z
Timezone+00:00
CalendarGregorian
Precision1 day
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Property / in defining formula
 

G
Property / in defining formula: / rank
 
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Property / in defining formula: / qualifier
 
Property / in defining formula
 

1
Property / in defining formula: / rank
 
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Property / in defining formula: / qualifier
 
Property / in defining formula
 

\cdot
Property / in defining formula: / rank
 
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Property / in defining formula: / qualifier
 
Property / in defining formula
 

x
Property / in defining formula: / rank
 
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Property / in defining formula: / qualifier
 
Property / in defining formula
 

y
Property / in defining formula: / rank
 
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Property / in defining formula: / qualifier
 
Property / in defining formula
 

z
Property / in defining formula: / rank
 
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Property / in defining formula: / qualifier
 
Property / De Agostini ID
 
gruppo+(algebra)
Property / De Agostini ID: gruppo+(algebra) / rank
 
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Property / De Agostini ID: gruppo+(algebra) / qualifier
 
Property / Treccani Vocabulary ID
 
gruppo
Property / Treccani Vocabulary ID: gruppo / rank
 
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Property / Treccani Vocabulary ID: gruppo / qualifier
 
Property / Treccani ID
 
gruppo
Property / Treccani ID: gruppo / rank
 
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Property / Treccani ID: gruppo / qualifier
 
Property / NicoNicoPedia ID
 
群(数学)
Property / NicoNicoPedia ID: 群(数学) / rank
 
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Property / Group Properties article ID
 
Group
Property / Group Properties article ID: Group / rank
 
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Property / Enciclopedia del Novecento ID
 
gruppi
Property / Enciclopedia del Novecento ID: gruppi / rank
 
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Property / Enciclopedia del Novecento ID: gruppi / qualifier
 
Property / Enciclopedia del Novecento ID: gruppi / qualifier
 
author name string: George W. Mackey
Property / Enciclopedia del Novecento ID: gruppi / qualifier
 
publication date: 1978
Timestamp+1978-01-01T00:00:00Z
Timezone+00:00
CalendarGregorian
Precision1 year
Before0
After0
Property / Larousse ID
 
divers/groupe/186120
Property / Larousse ID: divers/groupe/186120 / rank
 
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Property / Gran Enciclopèdia Catalana ID (former scheme)
 
0157361
Property / Gran Enciclopèdia Catalana ID (former scheme): 0157361 / rank
 
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Property / Gran Enciclopèdia Catalana ID
 
algebra-associativa
Property / Gran Enciclopèdia Catalana ID: algebra-associativa / rank
 
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Property / Metamath statement ID
 
df-grp
Property / Metamath statement ID: df-grp / rank
 
Normal rank

Latest revision as of 15:39, 29 July 2024

algebraic set with an invertible, associative internal operation admitting a neutral element
  • Group (algebra)
  • Group (math)
  • Mathematical group
  • mathematical group
  • algebraic group
Language Label Description Also known as
English
group
algebraic set with an invertible, associative internal operation admitting a neutral element
  • Group (algebra)
  • Group (math)
  • Mathematical group
  • mathematical group
  • algebraic group

Statements

Rubiks revenge tilt.jpg
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Cayley graph Q8.svg
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Identifiers

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/m/04xl4
1 reference
Group
0 references
topic/group-mathematics
0 references
5497
0 references
00041943n
1 reference
gruppe-mathematik
0 references
groupes-mathematiques-generalites
0 references
groupes-mathematiques-vue-d-ensemble
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93063749
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Group-Mathematics
1 reference
Group
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3908259
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군(대수학)
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group
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gruppe_-_matematikk
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06026202-n
1 reference
gruppo+(algebra)
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gruppo
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gruppo
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群(数学)
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Group
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gruppi
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divers/groupe/186120
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algebra-associativa
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df-grp
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