Hey everyone, im trying to figure this out, but no luck. Help would be much appreciated. So i am considering a 5-cycle: pi = (12345) in S_5. Its centralizer in S_5 is just <(pi)>, which is contained in A5. Therefore, when we restrict our main group to A_5, the conjugacy class that contained ALL permutations of cycle structure 5^1 gets split into two conjugacy classes. Now, a representative of the first one is obviously (12345) itself. Which brings me to my question:(adsbygoogle = window.adsbygoogle || []).push({});

Q: How to find the rep. of the 2nd conjugacy class?

I asked a group theorist, and here is his response:

(15)(24)(12345)(15)(24)=(54321)=[(12345)][/-1]. It follows that pi and pi^2 = (13524) are the 2 reps. In other words, (12345) and (13524) are NOT conjugate.

I am having trouble understanding exactly how this implies they are not conjugate.

Thanks in advance.

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# Finiding a representative of the 2nd conjugacy class in A_n

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