Results 1 to 4 of 4

Math Help - Abstract Algebra proof - cosets

  1. #1
    Senior Member
    Joined
    Apr 2008
    From
    Vermont
    Posts
    318

    Abstract Algebra proof - cosets

    Let H be a subgroup of G such that g^-1hg is an element of H for all g in G and all h in H. Show that every left coset gH is the same as the right coset Hg.



    need to show gh1=h2g
    I know I need to show this, but am unsure on how to.
    I know the whole set up excpet for this part and it confuses me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member rtblue's Avatar
    Joined
    Mar 2009
    From
    Birmingham, Alabama.
    Posts
    221
    maybe i'm just really bad at math, but... isn't this question in the wrong forum area?? just a though. After all.. it is abstract algebra, and i think MHF has a different forum section for those types of questions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    This should be in:

    Universtiy Math Help > Number Theory
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Quote Originally Posted by kathrynmath View Post
    Let H be a subgroup of G such that g^{-1}hg is an element of H for all g in G and all h in H. Show that every left coset gH is the same as the right coset Hg.



    need to show gh1=h2g
    I know I need to show this, but am unsure on how to.
    I know the whole set up excpet for this part and it confuses me.

    I'm a little rusty on the group theory stuf but I can recall the following:

    Every subgroup of an abelian group is normal. As your subgroup H is normal as  g^-1hg \in H maybe we can assume G is abelian (help anyone!)

    So if you can prove that G is in fact abelian then the following should follow for your cosets

    if H \triangleleft G then

     g_1Hg_2H

    operating on cosets

     \Rightarrow g_1g_2H
     \Rightarrow g_2g_1H

    I hope this helps some.
    Last edited by pickslides; April 28th 2009 at 03:53 AM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. abstract algebra proof
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: March 3rd 2010, 08:23 AM
  2. abstract algebra proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 27th 2010, 03:47 PM
  3. Proof-Abstract Algebra
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 22nd 2009, 07:48 PM
  4. Abstract algebra proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 30th 2008, 01:22 PM
  5. Abstract Algebra: Proof Help
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 31st 2008, 05:59 PM

Search Tags


/mathhelpforum @mathhelpforum