Thread: Question 11
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Old June 18th, 2009, 06:13 PM
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Quote:
Originally Posted by ThePerfectHacker View Post
I got this problem somewhere off the internet.
The problem and solution are not mine.
That is not a very pretty solution.

We know (ab)^2=(ba)^2. We know there is no element of order 2.

Suppose x^2=y^2; then (xy^{-1})^2=1. Since there is no element of order 2, we must have xy^{-1}=1; i.e. x=y.
Hence ab=ba for all a,b.
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