Show that is Abelian iff for every

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- Mar 29th 2009, 05:11 AMJimmy_WAbelian Group
Show that is Abelian iff for every

- Mar 29th 2009, 05:38 AMPaulRS
**Direct**: If is abelian then for all

If it is abelian then we can write: since commutativity holds

**Reciprocal**: If for all then is abelian

And: thus: and so it follows that it is commutative (Abelian)