Results 1 to 2 of 2

Math Help - Index of Permutation groups

  1. #1
    Junior Member
    Joined
    Oct 2007
    From
    Nova Scotia
    Posts
    48

    Index of Permutation groups

    Let H= {phi element of Sn | phi(n)=n}
    What's the index of H in Sn?

    the index of H in Sn = |Sn|/|H|
    and I know |Sn|= n!

    I was told the order of H is (n-1)! but i don't see how
    Could anyone help?
    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 frankdent1 View Post
    Let H= {phi element of Sn | phi(n)=n}
    What's the index of H in Sn?

    the index of H in Sn = |Sn|/|H|
    and I know |Sn|= n!

    I was told the order of H is (n-1)! but i don't see how
    Could anyone help?
    Basically H are all permutations that fix n. Therefore H can be regarded as the group of all permutations of \{ 1,2,...n-1\} i.e. isomorphic to S_{n-1} and so |H| = (n-1)!.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Permutation of groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 25th 2011, 01:13 AM
  2. Permutation Groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 3rd 2010, 04:04 PM
  3. Permutation Groups
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: August 15th 2010, 01:47 AM
  4. Permutation Groups
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 4th 2008, 05:14 PM
  5. Permutation Groups...
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: October 24th 2007, 08:55 PM

Search Tags


/mathhelpforum @mathhelpforum