Results 1 to 2 of 2

Math Help - Group Theory

  1. #1
    vogel
    Guest

    Group Theory

    Write down the group table for the premutuation group s3 and show that S3 is not abelian!!!!
    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 vogel View Post
    Write down the group table for the premutuation group s3 and show that S3 is not abelian!!!!
    Let,
    \sigma_1: 1\mapsto 1 , 2\mapsto 2, 3\mapsto 3.
    \sigma_2: 1\mapsto 2, 2\mapsto 3, 3\mapsto 1.
    \sigma_3: 1\mapsto 3, 2\mapsto 1, 3\mapsto 2.
    \sigma_4: 1\mapsto 2, 2\mapsto 1, 3\mapsto 3.
    \sigma_5: 1\mapsto 3, 2\mapsto 2, 3\mapsto 1.
    \sigma_6: 1\mapsto 1, 2\mapsto 3, 3\mapsto  2.

    Now if you let \alpha = \sigma_2 and \beta = \sigma_4. Then \{1,\alpha,\alpha^2 , \beta, \alpha \beta, \alpha^2 \beta \} expresses all S_3. Furthermore, confirm that \alpha \beta \not = \beta \alpha and you get what you wanted.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 4th 2009, 09:52 AM
  2. Quick questions on Group Theory - Cosets / Normal Group
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 16th 2009, 08:39 AM
  3. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  4. Group Theory Question, Dihedral Group
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2008, 10:36 AM
  5. Group Theory
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: July 12th 2007, 09:28 AM

/mathhelpforum @mathhelpforum