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!

Homework Help: Group theory: Conjugates, commutativity

  1. May 15, 2010 #1
    1. The problem statement, all variables and given/known data

    In S8, consider p= (1 3)(2 4 5 6) and q=(1 3)(2 4)(7 6 5)

    1. Find the number of conjugates of p and the number of conjugates of q
    2. Find the number of permutations that commute with p and the number that commute with q

    2. Relevant equations

    3. The attempt at a solution

    I think I've got myself really confused.

    1. For p, we are working in S8 so I initally count 8!
    I then divide by 2 as (1 3) = (3 1) and similarly divide by 4 because of the 4-cycle.
    The disjoint cycles are not the same length so my final answer is 8! / (4 x 2) = 7!

    For q, we have 8! / (2 x 2 x 3 x2) = 1680 where the final 2 is because we have 2 2-cycles.

    2. I'm not so sure about how to do this. I think it is asking me to find the size of the centralizer of each element but I don't know how to do this.
  2. jcsd
  3. May 19, 2010 #2
    I think you need to divide by 2 again for p because 7 and 8 could either be mapped to themselves or to each other without it affecting anything else
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook