Results 1 to 6 of 6

Math Help - homomorphic images

  1. #1
    Newbie
    Joined
    Dec 2006
    Posts
    5

    homomorphic images

    Last problem I can't figure out.

    Find all the homomorphic images of the following groups, D4 and Q.

    I would really really appreciate any help. Thanks in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    The homomorphic image of D_4 must be a subgroup of Q.

    Those all the possible homomorphic images are subgroups of Q.

    Thus,
    \{1\}
    \{1,-1\}
    \{1,-1,i,-i\}
    \{1,-1,j,-j\}
    \{1,-1,k,-k\}
    \{1,-1,i,-i,j,-j,k,-k\}

    You can also look heir.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2006
    Posts
    5
    So those are the homomorphic images of D4?

    What's Q then?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by nanotek887 View Post
    So those are the homomorphic images of D4?
    Yes, any homomorphic image must be one of those.
    What's Q then?
    That is the Octions,
    i^2=j^2=k^2=ijk=-1
    They are a subgroup of the multiplicative group of the Quaternions.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Dec 2006
    Posts
    5
    But are the homomorphic images of Q the subgroups of anything else like the one before?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Similarly the homomorphic images of Q are the subgroups of D4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A continuum of homomorphic images
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: June 4th 2010, 01:48 AM
  2. Homomorphic images of Z15.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 10th 2009, 01:16 PM
  3. Homomorphic images of D3.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 9th 2009, 05:07 PM
  4. Homomorphic images of D3.
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 28th 2009, 05:55 PM
  5. Homomorphic Images
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 18th 2006, 05:45 PM

Search Tags


/mathhelpforum @mathhelpforum