Centralizer of $\sigma\in S_n$

Asked Apr 28 '16 at 07:44

Active Apr 28 '16 at 07:44

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Let $\sigma\in S_n$ . Describe the centralizer of $\sigma$.

Thought: If I conjugate $\sigma$, then $\tau^{-1}\sigma\tau=\sigma.$ This means that $\tau$ is a power of $\sigma,$ and $<\sigma>\subseteq C_{S_n}(\sigma).$ What should I do after? I guess I just want to know what are the elements that commute with $\sigma$.

asked Apr 28 '16 at 07:44

Anonymous

1

Your "this means that..." is not correct in general. It is true that all powers of $\sigma$ commute with $\sigma$, but there might be other elements too. – Tobias Kildetoft Apr 28 '16 at 07:45
Are you familiar with the formula for what happens to a cycle when it is conjugated by some permutation? – Tobias Kildetoft Apr 28 '16 at 07:45

Centralizer of $\sigma\in S_n$

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