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Prove that G is a cyclic group

If an abelian group $G$ of order $10$ contains an element of order $5$ ,how can I prove that $G$ must be a cyclic group.

i am completely stuck on it. can anyone help?

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marked as duplicate by DonAntonio, Lukas Geyer, Micah, Norbert, Martin Argerami Nov 21 '12 at 5:56

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Do you know the Fundamental Theorem of Finite Abelian Groups yet? I think you can use that to prove that every Abelian group of order 10 is cyclic. –  Todd Wilcox Nov 21 '12 at 4:29

1 Answer 1

First, prove that any group of even order contains an element of order 2.

Now let $a$ be an element of order 2, let $b$ be an element of order $5$, and contemplate the order of $ab$.

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