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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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 $ab$.