Smart way to find the centralizer of (1,2)(3,4) in S_4. - MathOverflow [closed]most recent 30 from http://mathoverflow.net2013-06-19T06:18:14Zhttp://mathoverflow.net/feeds/question/47266http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/47266/smart-way-to-find-the-centralizer-of-1-23-4-in-s-4Smart way to find the centralizer of (1,2)(3,4) in S_4.Daniil2010-11-24T20:46:12Z2010-11-24T21:12:38Z
<p>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.</p>
<p>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 $A = C_{S_4}(g)$</p>