Prove that if is cyclic, then is abelian. (If is cyclic with generator , show that every element of can be written in the form for some integer and some in )

Z(G) = { g in G | gx = xg for every x in G}

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- Oct 4th 2008, 09:55 PMll2008cyclic
Prove that if is cyclic, then is abelian. (If is cyclic with generator , show that every element of can be written in the form for some integer and some in )

Z(G) = { g in G | gx = xg for every x in G} - Oct 5th 2008, 07:32 AMThePerfectHacker
Let . If then form . Thus, for . Likewise .

But then .