Wikidata

(Q83478)

English

group

algebraic set with an invertible, associative internal operation admitting a neutral element

  • Group (algebra)
  • Group (math)
  • Mathematical group
  • mathematical group
  • algebraic group
In more languages
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No label defined

No description defined

Statements

subclass of
monoid
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inverse semigroup
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Moufang loop
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groupoid
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epigroup
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algebraic structure
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loop
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image
Rubiks revenge tilt.jpg
600 × 600; 52 KB
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studied by
group theory
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category theory
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abstract algebra
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defining formula
(⋅):G×G→G∀x,y,z∈G:(x⋅y)⋅z=x⋅(y⋅z)∃1∈G∀x∈G:1⋅x=x⋅1=x∀x∈G∃y∈G:x⋅y=y⋅x=1
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has characteristic
closure
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associativity
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identity element
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inverse element
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Latin square property
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schematic
Cayley graph Q8.svg
385 × 385; 26 KB
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has part(s)
set
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binary operation
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identity element
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inverse
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different from
group
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Identifiers

NL CR AUT ID
ph180740
subject named as
grupy (algebra)
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BNCF Thesaurus ID
5497
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De Agostini ID
gruppo+(algebra)
subject named as
gruppo (algebra)
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LMFDB knowl ID
group
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MathWorld ID
Group
subject named as
Group
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nLab ID
group
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PlanetMath ID
Group
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Treccani ID
gruppo
subject named as
gruppo
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