## Smart way to find the centralizer of (1,2)(3,4) in S_4. [closed]

So I have $g = (1, 2)(3, 4) = \left(\begin{array}{cccc}1 & 2 & 3 & 4 \cr 2 & 1 & 4 & 3 \end{array}\right).$ I want to find $C_{S_4}(g)$. I know that I can just bruteforce'' the group, but I thought there might be a simplier way.

So far I think that $A = (1,2)^k(3,4)^n \in C_{S_4}(g)$ where $k, n \in \mathbb{Z}$, but I am not sure if $A = C_{S_4}(g)$

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 This looks like a homework question. – Nick S Nov 24 2010 at 20:55 Agreed, I've also voted to close. Daniil, please read the FAQ as there are suggestions for other forums where your question would be more appropriate. – Ryan Budney Nov 24 2010 at 20:57