Results 1 to 2 of 2

Math Help - surjective homomorphism

  1. #1
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1

    surjective homomorphism

    Hi All:

    I study a little abstravt algebra when I have time, which isn't very often. Here is one I was looking over and trying to show.

    I know that a homomorphism preserves operations. Example

    e^{x} is homorphic because e^{a}\cdot e^{b}=e^{a+b}. It has all the criteria of a homomorphism. It maps multiplication to addition.

    But, in general how can we show that if G is an abelian group (That is, ab=ba), Let f: \;\ G\rightarrow H be a surjective homomorphism of groups. Prove H is abelian.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Take a,b \in H such that a=f(x) and b=f(y) with x,y \in G then ab=f(x)f(y)=f(xy)=f(yx)=f(y)f(x)=ba And since f is surjective we're finished
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Well-defined, surjective ring homomorphism.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 16th 2011, 09:02 PM
  2. prove that if g o f is surjective then g is surjective
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: January 18th 2011, 10:41 AM
  3. Surjective Ring Homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: March 2nd 2010, 11:44 PM
  4. proving surjective homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 29th 2009, 07:04 PM
  5. Isomorphism of a surjective group homomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 7th 2008, 08:51 PM

Search Tags


/mathhelpforum @mathhelpforum