Results 1 to 2 of 2

Math Help - S12 Conjugate Elements

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    8

    Post S12 Conjugate Elements

    I'm trying to find the number of elements conjugate to (12)(34)(56789) in S12 but don't know how to go about it.

    Any help is much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by d_p_osters View Post
    I'm trying to find the number of elements conjugate to (12)(34)(56789) in S12 but don't know how to go about it.

    Any help is much appreciated.
    First we form a 5-cycle, there are 12 elements and we only choose 5 of them therefore there are {{12}\choose 5} ways to choose elements for a 5-cycle. Once we have chosen these 5 elements there are 4! ways of ordering them to form distinct 5-cycles. Now we need to form a 2-cycle, there are 7 elements left and we choose 2, therefore, {7\choose 2} and once those have been chosen we have {5\choose 2} for the remaining 2-cycle. Therefore, we get \frac{1}{2}\cdot 4! {{12}\choose 5}{7\choose 2}{5\choose 2} because we overcounted the 2-cycles twice i.e. (12345)(67)(89) is the same as (12345)(89)(67).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: December 10th 2011, 06:40 PM
  2. Replies: 8
    Last Post: November 27th 2011, 10:18 PM
  3. Conjugate?
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: September 14th 2009, 04:50 AM
  4. conjugate
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 16th 2009, 01:06 AM
  5. about conjugate
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 30th 2005, 06:12 PM

Search Tags


/mathhelpforum @mathhelpforum