Results 1 to 4 of 4

Math Help - Help with proof: If a is in S_n and commutes with every b in S_n, then a=(1)

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    13

    Help with proof: If a is in S_n and commutes with every b in S_n, then a=(1)

    Prove that for n>=3, if a is in S_n and commutes with every b in S_n,
    then a=(1)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jan 2009
    Posts
    153
    ab=ba ?

    Are a,b matrix ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    13
    Quote Originally Posted by math2009 View Post
    ab=ba ?

    Are a,b matrix ?
    No a and b are permutations in S_n.

    S_n being the symmetric group on n letters.
    Last edited by mr fantastic; February 11th 2009 at 09:56 PM. Reason: Merged posts
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by didact273 View Post
    Prove that for n>=3, if a is in S_n and commutes with every b in S_n, then a=(1)
    let (1) \neq a \in S_n. so there exist 1 \leq i \neq j \leq n with a(i)=j. since n \geq 3, there exists 1 \leq k \leq n such that k \notin \{i,j\}.

    now let b=(j \ \ k). then (ab)(i)=a(i)=j \neq k =b(j)=(ba)(i). thus ab \neq ba. \ \Box
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  2. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 10:07 PM
  3. proving that is A commutes, then its inverse does as well
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 3rd 2009, 07:08 AM
  4. commutes
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: October 22nd 2009, 07:56 AM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: April 14th 2008, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum