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Abelian group

475 bytes added, 19:48, 16 June 2007
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* A group is Abelian if its [[commutator subgroup]] is trivial.
==Examples==
 
[[Cyclic group]]s are good examples of Abelian groups. Further, any direct product of cyclic groups is also an Abelian group. Further, every [[finitely generated group|finitely generated]] Abelian group is obtained this way. This is the famous [[structure theorem for finitely generated Abelian groups]].
 
The structure theorem can be used to generate a complete listing of finite Abelian groups, as described here: [[classification of finite Abelian groups]].
==Facts==
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