Results 1 to 3 of 3

Math Help - Symmetric groups

  1. #1
    Junior Member
    Joined
    Jul 2008
    Posts
    54

    Exclamation Symmetric groups

    Help me to prove this,

    Show that if and with then .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie Catherine Morland's Avatar
    Joined
    Jul 2008
    Posts
    17
    For each r\in\{1,\ldots,n\}, let X_r be the set of all permutations in S_n which fix r. Then X_r is a set of permutations on n-1 numbers, so |X_r|=(n-1)! - hence |S_n:X_r|=n, and there is a one-to-one correspondence between X_r and S_{n-1}
    Last edited by Catherine Morland; August 6th 2008 at 12:16 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Here is a similar question I was thinking of.
    Find all the index n subgroups of S_n.
    Is it S(1), ... S(n) - where S(i) are permutations which fix i?
    I know this is true for n=3,4.
    But how do we prove it if it is true?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orders of elements in Symmetric groups
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: March 30th 2010, 03:39 PM
  2. symmetric groups 2
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2009, 10:13 AM
  3. symmetric groups 3
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2009, 10:06 AM
  4. Symmetric Groups Questions
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 22nd 2009, 02:00 PM
  5. Subgrounds of Symmetric Groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 10th 2008, 09:11 PM

Search Tags


/mathhelpforum @mathhelpforum