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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
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