group (Q1253): Difference between revisions

@@ Property / image @@
+Rubiks revenge tilt.jpg
@@ Property / image: Rubiks revenge tilt.jpg / rank @@
+Normal rank
@@ Property / subclass of @@
+monoid
@@ Property / subclass of: monoid / rank @@
+Normal rank
@@ Property / subclass of @@
+inverse semigroup
@@ Property / subclass of: inverse semigroup / rank @@
+Normal rank
@@ Property / subclass of @@
+Moufang loop
@@ Property / subclass of: Moufang loop / rank @@
+Normal rank
@@ Property / subclass of @@
+groupoid
@@ Property / subclass of: groupoid / rank @@
+Normal rank
@@ Property / subclass of @@
+epigroup
@@ Property / subclass of: epigroup / rank @@
+Normal rank
@@ Property / subclass of @@
+algebraic structure
@@ Property / subclass of: algebraic structure / rank @@
+Normal rank
@@ Property / subclass of @@
+group object
@@ Property / subclass of: group object / rank @@
+Normal rank
@@ Property / subclass of: group object / qualifier @@
+of: category of sets
@@ Property / subclass of @@
+loop
@@ Property / subclass of: loop / rank @@
+Normal rank
@@ Property / Freebase ID @@
+/m/04xl4
@@ Property / Freebase ID: /m/04xl4 / rank @@
+Normal rank
@@ Property / Freebase ID: /m/04xl4 / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / topic's main category @@
+Q2687
@@ Property / topic's main category: Q2687 / rank @@
+Normal rank
@@ Property / topic's main category: Q2687 / reference @@
+imported from Wikimedia project: German Wikipedia
@@ Property / GND ID @@
+4022379-6
@@ Property / GND ID: 4022379-6 / rank @@
+Normal rank
@@ Property / GND ID: 4022379-6 / reference @@
+imported from Wikimedia project: German Wikipedia
@@ Property / Commons category @@
+Group theory
@@ Property / Commons category: Group theory / rank @@
+Normal rank
@@ Property / Commons category: Group theory / reference @@
+imported from Wikimedia project: Arabic Wikipedia
@@ Property / MathWorld ID @@
+Group
@@ Property / MathWorld ID: Group / rank @@
+Normal rank
@@ Property / Encyclopædia Britannica Online ID @@
+topic/group-mathematics
@@ Property / Encyclopædia Britannica Online ID: topic/group-mathematics / rank @@
+Normal rank
+subject named as: group
@@ Property / BNCF Thesaurus ID @@
@@ Property / BNCF Thesaurus ID: 5497 / rank @@
+Normal rank
@@ Property / has list @@
+Examples of groups
@@ Property / has list: Examples of groups / rank @@
+Normal rank
@@ Property / has characteristic @@
+closure
@@ Property / has characteristic: closure / rank @@
+Normal rank
@@ Property / has characteristic @@
+associativity
@@ Property / has characteristic: associativity / rank @@
+Normal rank
@@ Property / has characteristic @@
+identity element
@@ Property / has characteristic: identity element / rank @@
+Normal rank
@@ Property / has characteristic @@
+inverse element
@@ Property / has characteristic: inverse element / rank @@
+Normal rank
@@ Property / has characteristic @@
+Latin square property
@@ Property / has characteristic: Latin square property / rank @@
+Normal rank
@@ Property / studied in @@
+group theory
@@ Property / studied in: group theory / rank @@
+Normal rank
@@ Property / studied in @@
+category theory
@@ Property / studied in: category theory / rank @@
+Normal rank
@@ Property / studied in @@
+abstract algebra
@@ Property / studied in: abstract algebra / rank @@
+Normal rank
@@ Property / defining formula @@
+ ${\begin{aligned}&(\cdot )\colon G\times G\to G\\&\forall x,y,z\in G\colon (x\cdot y)\cdot z=x\cdot (y\cdot z)\\&\exists 1\in G\forall x\in G\colon 1\cdot x=x\cdot 1=x\\&\forall x\in G\exists y\in G\colon x\cdot y=y\cdot x=1\end{aligned}}$ 
\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}
+Normal rank
@@ Property / BabelNet ID @@
+00041943n
@@ Property / BabelNet ID: 00041943n / rank @@
+Normal rank
@@ Property / BabelNet ID: 00041943n / reference @@
+stated in: BabelNet
@@ Property / properties for this type @@
+group cardinality
@@ Property / properties for this type: group cardinality / rank @@
+Normal rank
@@ Property / Brockhaus Enzyklopädie online ID @@
+gruppe-mathematik
@@ Property / Brockhaus Enzyklopädie online ID: gruppe-mathematik / rank @@
+Normal rank
@@ Property / Encyclopædia Universalis ID @@
+groupes-mathematiques-generalites
+Normal rank
@@ Property / Encyclopædia Universalis ID @@
+groupes-mathematiques-vue-d-ensemble
+Normal rank
@@ Property / has part(s) @@
+set
@@ Property / has part(s): set / rank @@
+Normal rank
@@ Property / has part(s) @@
+binary operation
@@ Property / has part(s): binary operation / rank @@
+Normal rank
@@ Property / has part(s) @@
+identity element
@@ Property / has part(s): identity element / rank @@
+Normal rank
@@ Property / has part(s) @@
+inverse
@@ Property / has part(s): inverse / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+93063749
@@ Property / Microsoft Academic ID: 93063749 / rank @@
+Normal rank
@@ Property / topic's main template @@
+Template:Group navbox
@@ Property / topic's main template: Template:Group navbox / rank @@
+Normal rank
@@ Property / topic's main template: Template:Group navbox / reference @@
+inferred from: Template:Group navbox
@@ Property / KBpedia ID @@
+Group-Mathematics
@@ Property / KBpedia ID: Group-Mathematics / rank @@
+Normal rank
@@ Property / KBpedia ID: Group-Mathematics / reference @@
+stated in: KBpedia
retrieved: 9 July 2020Timestamp +2020-07-09T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2020-07-09T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / different from @@
+group
@@ Property / different from: group / rank @@
+Normal rank
@@ Property / PlanetMath ID @@
+Group
@@ Property / PlanetMath ID: Group / rank @@
+Normal rank
@@ Property / Online PWN Encyclopedia ID @@
+3908259
@@ Property / Online PWN Encyclopedia ID: 3908259 / rank @@
+Normal rank
@@ Property / Namuwiki ID @@
+군(대수학)
@@ Property / Namuwiki ID: 군(대수학) / rank @@
+Normal rank
@@ Property / schematic @@
+Cayley graph Q8.svg
@@ Property / schematic: Cayley graph Q8.svg / rank @@
+Normal rank
@@ Property / Encyclopedia of Mathematics article ID @@
+Group
@@ Property / Encyclopedia of Mathematics article ID: Group / rank @@
+Normal rank
@@ Property / nLab ID @@
+group
@@ Property / nLab ID: group / rank @@
+Normal rank
@@ Property / Store norske leksikon ID @@
+gruppe_-_matematikk
@@ Property / Store norske leksikon ID: gruppe_-_matematikk / rank @@
+Normal rank
@@ Property / WordNet 3.1 Synset ID @@
+06026202-n
@@ Property / WordNet 3.1 Synset ID: 06026202-n / rank @@
+Normal rank
@@ Property / WordNet 3.1 Synset ID: 06026202-n / reference @@
+stated in: GF WordNet
@@ Property / on focus list of Wikimedia project @@
+Wikipedia:Vital articles/Level/4
+Normal rank
+point in time: 31 October 2022Timestamp +2022-10-31T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
-Timestamp
++2022-10-31T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
 Before
 After
@@ Property / in defining formula @@
+ $G$ 
G
@@ Property / in defining formula: $G$ / rank @@
+Normal rank
@@ Property / in defining formula: $G$ / qualifier @@
+symbol represents: group
@@ Property / in defining formula @@
+ $1$ 
1
@@ Property / in defining formula: $1$ / rank @@
+Normal rank
@@ Property / in defining formula: $1$ / qualifier @@
+symbol represents: multiplicative identity
@@ Property / in defining formula @@
+ $\cdot$ 
\cdot
@@ Property / in defining formula: $\cdot$ / rank @@
+Normal rank
@@ Property / in defining formula: $\cdot$ / qualifier @@
+symbol represents: group operation
@@ Property / in defining formula @@
+ $x$ 
x
@@ Property / in defining formula: $x$ / rank @@
+Normal rank
@@ Property / in defining formula: $x$ / qualifier @@
+symbol represents: element
@@ Property / in defining formula @@
+ $y$ 
y
@@ Property / in defining formula: $y$ / rank @@
+Normal rank
@@ Property / in defining formula: $y$ / qualifier @@
+symbol represents: element
@@ Property / in defining formula @@
+ $z$ 
z
@@ Property / in defining formula: $z$ / rank @@
+Normal rank
@@ Property / in defining formula: $z$ / qualifier @@
+symbol represents: element
@@ Property / De Agostini ID @@
+gruppo+(algebra)
@@ Property / De Agostini ID: gruppo+(algebra) / rank @@
+Normal rank
@@ Property / De Agostini ID: gruppo+(algebra) / qualifier @@
+subject named as: gruppo
@@ Property / Treccani Vocabulary ID @@
+gruppo
@@ Property / Treccani Vocabulary ID: gruppo / rank @@
+Normal rank
@@ Property / Treccani Vocabulary ID: gruppo / qualifier @@
+subject named as: gruppo
@@ Property / Treccani ID @@
+gruppo
@@ Property / Treccani ID: gruppo / rank @@
+Normal rank
@@ Property / Treccani ID: gruppo / qualifier @@
+subject named as: gruppo
@@ Property / NicoNicoPedia ID @@
+群(数学)
@@ Property / NicoNicoPedia ID: 群(数学) / rank @@
+Normal rank
@@ Property / Group Properties article ID @@
+Group
@@ Property / Group Properties article ID: Group / rank @@
+Normal rank
@@ Property / Enciclopedia del Novecento ID @@
+gruppi
@@ Property / Enciclopedia del Novecento ID: gruppi / rank @@
+Normal rank
@@ Property / Enciclopedia del Novecento ID: gruppi / qualifier @@
+subject named as: Gruppi
@@ Property / Enciclopedia del Novecento ID: gruppi / qualifier @@
+author name string: George W. Mackey
@@ Property / Enciclopedia del Novecento ID: gruppi / qualifier @@
+publication date: 1978Timestamp +1978-01-01T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 year
Before 0
After 0
-Timestamp
++1978-01-01T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+year
 Before
 After
@@ Property / Larousse ID @@
+divers/groupe/186120
@@ Property / Larousse ID: divers/groupe/186120 / rank @@
+Normal rank
@@ Property / Gran Enciclopèdia Catalana ID (former scheme) @@
+0157361
@@ Property / Gran Enciclopèdia Catalana ID (former scheme): 0157361 / rank @@
+Normal rank
@@ Property / Gran Enciclopèdia Catalana ID @@
+algebra-associativa
@@ Property / Gran Enciclopèdia Catalana ID: algebra-associativa / rank @@
+Normal rank
@@ Property / Metamath statement ID @@
+df-grp
@@ Property / Metamath statement ID: df-grp / rank @@
+Normal rank

Latest revision as of 16:39, 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