# 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 [duplicate]

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