Results 1 to 2 of 2

Math Help - Subgrounds of Symmetric Groups

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    15

    Subgrounds of Symmetric Groups

    I'm trying to find all of the subgroups of the symmetric S_{3}. But am not sure how to generate these groups as all of the properties of groups must be satisfied.

    I am thinking it is something along the lines of:
    {(123)->(123)} (no change)
    {(123)->(123), (312), (231)}
    {(123)->(123),(132), (213), (321)}

    Is this the right track? Or am out out in left field?
    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 apsis View Post
    I'm trying to find all of the subgroups of the symmetric S_{3}. But am not sure how to generate these groups as all of the properties of groups must be satisfied.

    I am thinking it is something along the lines of:
    {(123)->(123)} (no change)
    {(123)->(123), (312), (231)}
    {(123)->(123),(132), (213), (321)}

    Is this the right track? Or am out out in left field?
    The subgroups are \{ e \}, \left< (12) \right>, \left< (13)\right>, \left< (23) \right>, \left< (123) \right>,S_3.
    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, 02:39 PM
  2. symmetric groups 2
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2009, 09:13 AM
  3. symmetric groups 3
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 24th 2009, 09:06 AM
  4. Symmetric Groups Questions
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 22nd 2009, 01:00 PM
  5. Symmetric groups
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: August 6th 2008, 10:07 AM

Search Tags


/mathhelpforum @mathhelpforum