1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Needs a counterexample for homomorphisms

  1. Oct 2, 2008 #1
    1. The problem statement, all variables and given/known data
    Let A, B be groups and A' and B' be normal subgroups of A and B respectively. Let f: A --> B be a homomorphism with f(A') being a subgroup of B'. There is a well-defined homomorphism g: A/A' -----> B/B' defined by g: aA' ---> f(a)B'

    Find an example in which f is injective, but g is not injective.

    2. Relevant equations
    I've proven that g is a well-defined homomorphism and that if f is surjective, then g is surjective.


    3. The attempt at a solution
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Needs a counterexample for homomorphisms
  1. Answer need checking! (Replies: 0)

  2. Need help (Replies: 0)

Loading...