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I'm having some trouble trying to solve this question.. Any advice/help is appreciated!

1. The problem statement, all variables and given/known data

Suppose that a and b belong to a group such that:

|a| = 4, |b| = 2, and suppose a^{3}b=ba

Find the order of ab.

2. Relevant equations

3. The attempt at a solution

So I am unsure of which theorems I should be looking at... but anyways...... my horrible attempt:

so a,b are in G.

|ab| = (ab)^{n}= 1

Let n = order(ab), a^{n}b^{n}= 1 --> a^{n}=b^{-n}

I don't know if I should continue from this point because I don't know how exactly I would go about finding the order.

I think |ab| = |ba|, yes or no?

If it does then I'm guessing I can use that to find the order of a^{3}b?

Any hints or suggestions on how?

Thank you.

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# Homework Help: Order of an element in a group

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