Results 1 to 2 of 2

Math Help - Subgroups of S4

  1. #1
    nhk
    nhk is offline
    Junior Member
    Joined
    Apr 2010
    Posts
    43

    Subgroups of S4

    Find all the 3-Sylow subgroups of S4. I am having a real hard time getting the idea behind Sylow subgroups. Can someone help me with this please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2010
    Posts
    95
    Quote Originally Posted by nhk View Post
    Find all the 3-Sylow subgroups of S4. I am having a real hard time getting the idea behind Sylow subgroups. Can someone help me with this please?
    I'll assume S4 as the symmetric group of degree 4.

    The possible order of a 3-Sylow subgroup of S_4 should be 3, i.e., 3^1 \mid 24 and 3^k \nmid 24 for k \geq 2.

    The order 3 subgroups of S_4 are simply the cyclic groups of order 3.

    <(1 2 3)>, <(1 3 4)>, <(2 3 4)>, and <(1 2 4)>.

    The number of 3-Sylow subgroups of S_4 is 4, which agrees to the third Sylow theorem, i.e., 4 \mid 24 and 4=1\cdot3 + 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Subgroups and Intersection of Normal Subgroups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 1st 2010, 09:12 PM
  2. subgroups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 28th 2010, 03:06 AM
  3. subgroups and normal subgroups
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 19th 2010, 04:30 PM
  4. Subgroups and Normal Subgroups
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 9th 2009, 09:36 AM
  5. Subgroups and normal subgroups
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: October 13th 2007, 05:35 PM

Search Tags


/mathhelpforum @mathhelpforum