Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By HallsofIvy

Thread: group homomorphism

  1. #1
    Newbie
    Joined
    Dec 2016
    From
    maharashtra
    Posts
    5

    group homomorphism

    Consider the group homomorphism. f: M2(R) to R given by f(A)= trace(A). Then the kernel of f is isomorphic to which group?Any idea? Plz help me thanks in advance!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,406
    Thanks
    2886

    Re: group homomorphism

    Do you understand what you are told here? M2(R) is the set of 2 by 2 invertible matrices. The matrix \begin{pmatrix}a & b \\ c & d \end{pmatrix}, such that ad- bc is not 0, is mapped to a+ d. In particular, the "kernel" of this homomorphism is the set of all matrices \begin{pmatrix}a & b \\ c & -a \end{pmatrix} for which -bc- a^2 is not 0.
    Thanks from snehal
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Group Homomorphism
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Oct 27th 2012, 12:56 AM
  2. homomorphism from a group Z36 to a group of order 24
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Mar 23rd 2012, 10:35 AM
  3. group homomorphism
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Oct 22nd 2010, 05:51 AM
  4. Group homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 5th 2010, 02:24 AM
  5. group homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: Jan 19th 2010, 09:05 PM

/mathhelpforum @mathhelpforum