Results 1 to 2 of 2

Math Help - About cosets Theorem

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    6

    About cosets Theorem

    I know if G is a group, H is a subgroup of G, and g is an element of G

    gH= {gh: h an element of H} is a left coset of H in G

    But just cant apply to the Questions Help me !
    Thanks


    1) consider the element X=(1423) ∈ S₄

    ⅰ) Write down the elements of <X>
    ⅱ)Write down the elements of the left coset<12><X>
    ⅲ)Write down the elements of the left coset<123><X>
    ⅳ)Determine the index [S₄: (X)]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Hyungmin View Post
    I know if G is a group, H is a subgroup of G, and g is an element of G

    gH= {gh: h an element of H} is a left coset of H in G

    But just cant apply to the Questions Help me !
    Thanks


    1) consider the element X=(1423) ∈ S₄

    ⅰ) Write down the elements of <X>
    ⅱ)Write down the elements of the left coset<12><X>
    ⅲ)Write down the elements of the left coset<123><X>
    ⅳ)Determine the index [S₄: (X)]
    Write down the elements? I'm sure you can do that. Similarly, the next two are just computation. The last can be seen as a result of finding all the cosets or employing Lagrange's theorem considering that \left|\left\langle (1423)\right \rangle\right|=4 we have that \left[S_4:\left\langle (1423)\right\rangle\right]=\frac{4!}{4}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 22nd 2009, 02:40 PM
  2. Cosets and Lagrange's Theorem
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 15th 2009, 07:36 PM
  3. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 4th 2009, 05:02 PM
  4. Cosets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 9th 2008, 03:22 PM
  5. cosets
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 6th 2007, 01:59 PM

Search Tags


/mathhelpforum @mathhelpforum