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I'm a bit confused about this proof that $A_n$ is simple for $n > 4$. The conclusion of the second paragraph is not clear to me. Why is that $\sigma'\sigma^{-1}$ fixing fewer symbols than $\sigma$ a contradiction?

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    It appears to be a typo. What is meant is ***more*** symbols are fixed by $\sigma'\sigma^{-1}$, since $2$ is fixed as well as all fixed points of $\sigma$.2012-10-31

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