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Abelian group

50 bytes added, 14:34, 12 July 2012
Definition
An '''abelian group''' is a [[group]] where any two elements commute. In symbols, a [[group]] <math>G</math> is termed '''abelian''' if for any elements <math>x</math> and <math>y</math> in <math>G</math>, <math>xy = yx</math> (here <math>xy</math> denotes the product of <math>x</math> and <math>y</math> in <math>G</math>). Note that <math>x,y</math> are allowed to be equal, though equal elements commute anyway, so we can restrict attention if we wish to unequal elements.
 
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* A group is abelian if its [[defining ingredient::center]] is the whole group.
* A group is abelian if its [[defining ingredient::commutator derived subgroup]] is trivial.
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