Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
    
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
add comment

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1 Answer

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 $ab$.

share|improve this answer
add comment

Not the answer you're looking for? Browse other questions tagged or ask your own question.