1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Permutation group conjugates

  1. Mar 11, 2012 #1
    Hey,

    I just have a small question regarding the conjugation of permutation groups.

    Two permutations are conjugates iff they have the same cycle structure.

    However the conjugation permutation, which i'll call s can be any cycle structure. (s-1 a s = b) where a, b and conjugate permutations by s

    My question is, how can you find out how many conjugation permutations (s) are within a group which also conjugate a and b.

    So for example (1 4 2)(3 5) conjugates to (1 2 4)(3 5) under s = (2 4), how could you find the number of alternate s's in the group of permutations with 5 objects?

    Would it be like

    (1 4 2) (3 5) is the same as (2 1 4) (35) which gives a different conjugation permutation,
    another is

    (4 1 2)(3 5), then these two with (5 3) instead of ( 3 5),

    so that gives 6 different arrangements, and similarly (1 2 4) (35) has 6 different arrangements,

    and each arrangement would produce a different conjugation permutation (s)

    so altogether there would be 6x6=36 permutations have the property that
    s-1 a s = b ?


    Thanks in advance
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: Permutation group conjugates
  1. Permutation Groups (Replies: 3)

Loading...