Find the centralizer of (1 2) in S5. (Conjugation in the symmetric group) I have no idea how to solve this kind of problem. Can you show me the method? Thanks!
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You are looking for permutations $\sigma\in S_5$, such that $\sigma \circ (1\ 2)\circ \sigma^{-1}= (1\ 2)$. Carrying out function composition you can see that LHS is another transposition, namely the one swapping $\sigma(1)$ with $\sigma(2)$. Now try to find out those for which it is the same as swapping 1 with 2.
P Vanchinathan
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It would be the elements that do not contain (1) or (2) in their cycles + the identity element. Correct? – user569685 Aug 31 '20 at 20:10