Results 1 to 5 of 5

Math Help - [SOLVED] Normalizer and Equality of left, right cosets.

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    195

    [SOLVED] Normalizer and Equality of left, right cosets.



    I think this is a huge assumption to make, but I think this is true. I'm not sure how to bridge the gap.

    I'm still kind of confused why for some group H and some h \in H, aha^{-1} = h' \in H with h' \neq h isn't a possibility.
    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
    What's the huge assumption?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Oct 2009
    Posts
    195
    Quote Originally Posted by Drexel28 View Post
    What's the huge assumption?
    aHa^{-1} = H \implies aH = Ha

    Edit: Maybe thats not a huge assumption since

    aHa^{-1} = H \implies aHa^{-1}(a) = H(a) \implies aH = Ha.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by davismj View Post
    aHa^{-1} = H \implies aH = Ha
    aHa^{-1}=H\implies aH=Ha?

    If ah\in aH then aha^{-1}\in aHa^{-1}=H and thus aha^{-1}=h' for some h'\in H and thus ah=h'a in particular ah\in Ha so that aH\subseteq Ha. The reverse inclusion is similar.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2009
    Posts
    195
    Quote Originally Posted by Drexel28 View Post
    aHa^{-1}=H\implies aH=Ha?

    If ah\in aH then aha^{-1}\in aHa^{-1}=H and thus aha^{-1}=h' for some h'\in H and thus ah=h'a in particular ah\in Ha so that aH\subseteq Ha. The reverse inclusion is similar.
    Thanks bud.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Left and Right cosets.
    Posted in the Advanced Algebra Forum
    Replies: 12
    Last Post: February 2nd 2010, 01:35 PM
  2. Left cosets
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 11th 2010, 09:43 AM
  3. left and right cosets
    Posted in the Advanced Algebra Forum
    Replies: 10
    Last Post: November 4th 2009, 08:42 PM
  4. Left and Right Cosets
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 22nd 2009, 11:06 PM
  5. right and left cosets
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 15th 2008, 06:08 PM

Search Tags


/mathhelpforum @mathhelpforum