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Conjugacy classes

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Given (1,2,3)(4,5,6) in S_6, compute all the elements in the centralizers.


    2. Relevant equations

    Well I know that cycle structure is preserved. Etc. I just want to know if there is a less brute force way to compute all 18 instead of going:

    (1,2,3)(4,5,6)(1,2,3)(4,5,6)(1,2,3)(4,5,6)=(1,2,3)(4,5,6)
    (2,3,1)(4,5,6)(1,2,3)(4,5,6)(2,3,1)(4,5,6)=(2,3,1)(4)(5)(6)
    etc.
    Also, for some reason I haven't been able to get all 18
     
  2. jcsd
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