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Redak 1: Redak 1:
[[grupa]] s [[komutativna operacija|komutativnom operacijom]]
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{{HNM2 pojam
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|naziv=komutativna grupa
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|naziv2=komutativna-grupa
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|Struna_ID=30704
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|obrađivač=Nenad Antonić
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|faza_obrade=zaključaj naziv
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|definicija=grupa s komutativnom operacijom
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|skolska_definicija=
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|napomena=
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|vrsta_riječi=višerječni naziv
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|rod=nema
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|broj=nema
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|simbol=
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|kontekst=
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|dopušteni=Abelova grupa
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|skraćeni=
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|en=commutative group
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|nepreporučeni=
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|podređeni=
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|suprotnica=
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|zastarjeli=}}
  
A [[group]] for which the [[binarna operacija|binary operation]] is [[commutative binary operation|commutative]]
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{{WMW
 
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|Struna_ID=30704
An Abelian group is a group for which the elements commute (i.e., $AB=BA$ for all elements $A$ and $B$). Abelian groups therefore correspond to groups with symmetric multiplication tables.
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|naziv=Abelian group
 
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|klasifikacija=Algebra > Group Theory > Groups >
Abelova grupa - dopušteni
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|definicija=An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication tables.
 
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|cite= Weisstein, Eric W. "Abelian Group." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/AbelianGroup.html
Struna ID: 30704
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|napomena=All cyclic groups are Abelian, but an Abelian group is not necessarily cyclic. All subgroups of an Abelian group are normal. In an Abelian group, each element is in a conjugacy class by itself, and the character table involves powers of a single element known as a group generator.
 
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|see_also=Finite Group, Group Theory, Kronecker Decomposition Theorem, Partition Function P, Ring}}
Abelova grupa = Abelian group (EN)
 
 
 
komutativna grupa = commutative group (EN)
 
 
 
komutativna grupa = groupe commutatif (FR)
 
 
 
Abelova grupa = groupe abélien (FR)
 
 
 
Povezani pojmovi:
 
 
 
finite group group theory  | Kronecker decomposition theorem  |  partition function P |  ring
 
 
 
Klasifikacija:
 
 
 
MAthWorld: Algebra > Group Theory > Groups
 
 
 
MSC-2010: group theory and generalizations (20-XX)
 
 
 
Educational grade level: college level
 

Inačica od 19:14, 19. listopada 2014.

Definicija: grupa s komutativnom operacijom

Dopušteni nazivi: Abelova grupa

Engleske istovrijednice: commutative group


Struna ID: 30704

Obrađivač: Nenad Antonić

Faza obrade: zaključaj naziv

Vrsta riječi: višerječni naziv Rod: nema Broj: nema


Cilj projekta "Hrvatsko nazivlje u matematici" je na jednom mjestu prikupiti i obraditi sve hrvatske nazive koji na izravan ili neizravan način imaju veze s matematikom. Ako želite na bilo koji način doprinijeti ostvarenju ciljeva ovog projekta, molim javite se voditelju projekta na adresu goran.igaly@math.hr


Traženi pojmovi



WMW naziv: Abelian group

WMW klasifikacija: Algebra > Group Theory > Groups >

WMW definicija: An Abelian group is a group for which the elements commute (i.e., AB=BA for all elements A and B). Abelian groups therefore correspond to groups with symmetric multiplication tables.

WMW napomena: All cyclic groups are Abelian, but an Abelian group is not necessarily cyclic. All subgroups of an Abelian group are normal. In an Abelian group, each element is in a conjugacy class by itself, and the character table involves powers of a single element known as a group generator.


WMW See also: Finite Group, Group Theory, Kronecker Decomposition Theorem, Partition Function P, Ring


Izvor: Weisstein, Eric W. "Abelian Group." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/AbelianGroup.html

Struna ID: 30704