Results 1 to 4 of 4

Math Help - Abstract Algebra, permutation groups

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    36

    Abstract Algebra, permutation groups

    I dont even know where to start on this one.

    Show for n>2, the group of permutations on n elements is non-abelian.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by ziggychick View Post
    I dont even know where to start on this one.

    Show for n>2, the group of permutations on n elements is non-abelian.

    Thanks!
    (1 \ 2)(2 \ 3)=(1 \ 2 \ 3) \neq (1 \ 3 \ 2)=(2 \ 3)(1 \ 2). now answer this simple question:

    imagine for a second that all symmetric groups were abelian, then is it true that every group would be abelian? (how cool would that be! )
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2008
    Posts
    36
    Ok. Since every group is isomorphic to some permutation group, if all the permutation groups were abelian, than every group would also be abelian. (That would be super cool. Peace out matrices)

    I think I know what to do now. Thanks so much!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by NonCommAlg View Post
    imagine for a second that all symmetric groups were abelian, then is it true that every group would be abelian? (how cool would that be! )
    It would mean all of group theory can be summarized in 60 pages.

    Show for n>2
    I just want to add, since NonCommAlg was implicit about this, this condition is necessary to have a third element. If n>=2 then writing (12)(23) is not allowed since there is no third element. That is why this condition is necessary.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Abstract Algebra-Groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 30th 2009, 12:39 PM
  2. Abstract Algebra: Groups
    Posted in the Advanced Algebra Forum
    Replies: 14
    Last Post: April 6th 2008, 07:52 PM
  3. Abstract Algebra: Orders of Groups
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 5th 2008, 07:48 AM
  4. Abstract Algebra: Groups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 5th 2008, 03:13 AM
  5. Abstract Algebra: Groups
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: February 11th 2008, 09:39 AM

Search Tags


/mathhelpforum @mathhelpforum