Show that every cyclic group Cn of order n is abelian. (Moreover, show that if G is a group, so is GxG)© BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf
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 ...
It is shown that every cyclic group Cn of order n is abelian. The proof is concise.