View source for Abelian group

<font color="orange">زمرة أبيلية</font> (''Ar''). <font color="blue">Groupe abélien</font> (''Fr''). <font color="red">Abelsche Gruppe</font> (''Ge''). <font color="black">Gruppo abeliano</font> (''It''). <font color="purple">アーベル群</font> (''Ja''). <font color="brown">Абелева группа</font> (''Ru''). <font color="green">Grupo abeliano</font> (''Sp''). 

An '''Abelian group''', also called a ''commutative group'', is a group (''G'', * ) such that ''g''<sub>1</sub> * ''g''<sub>2</sub> = ''g''<sub>2</sub> * ''g''<sub>1</sub> for all ''g''<sub>1</sub> and ''g''<sub>2</sub> in ''G'', where * is a [[binary operation]] in ''G''. This means that the order in which the binary operation is performed does not matter, and any two elements of the group commute.

Groups that are not commutative are called non-abelian (rather than non-commutative).

Abelian groups are named after Niels Henrik Abel.

[[Category:Fundamental crystallography]]