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I have just begun studying the group $S_n$ and I am having trouble with the cycle notation so this problem seems a bit hard. Any help will be deeply appreciated:

If $a \in S_n$ is an $n$-cycle or an $(n-1)$-cycle then the centralizer of $a$ is equal to the cyclic group $\langle a\rangle$.

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    Hint: if you conjugate a cycle $a$ by another cycle $b$, all you have to do is apply the $b$ permutation to the numbers in cycle $a$. For example, $(1234)^{(12)}=(2134)$. (You should prove this if you plan to use it!)2012-11-12

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