# Cyclic Groups

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Show that every cyclic group Cn of order n is abelian. (Moreover, show that if G is a group, so is GxG)

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#### Solution Preview

1. Cn is a cyclic group of order n. Then Cn=<a>, where a is a generator of Cn. So for any elements x,y in Cn, we have x=a^i, y=a^j for some integer i,j. Thus ...

#### Solution Summary

It is shown that every cyclic group Cn of order n is abelian. The proof is concise.

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