Razlika između inačica stranice »Komutativna grupa«
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|naziv=Abelian group | |naziv=Abelian group | ||
|klasifikacija=Algebra > Group Theory > Groups > | |klasifikacija=Algebra > Group Theory > Groups > | ||
| − | |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. | + | |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. |
|cite= Weisstein, Eric W. "Abelian Group." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/AbelianGroup.html | |cite= Weisstein, Eric W. "Abelian Group." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/AbelianGroup.html | ||
|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. | |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. | ||
|see_also=Finite Group, Group Theory, Kronecker Decomposition Theorem, Partition Function P, Ring}} | |see_also=Finite Group, Group Theory, Kronecker Decomposition Theorem, Partition Function P, Ring}} | ||
Inačica od 19:16, 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
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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