Results 1 to 2 of 2

Math Help - Needs Counterexample for homomorphisms

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    3

    Needs Counterexample for homomorphisms

    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.


    I've proven that g is a well-defined homomorphism and that if f is surjective, then g is surjective; but don't really know how to go with this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by playa007 View Post
    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.
    How about A=B=\mathbb{Z}, f = identity map, A' = {multiples of 4}, B' = {multiples of 2}?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Counterexample Help
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: October 5th 2010, 08:24 AM
  2. Counterexample
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 26th 2010, 09:17 AM
  3. Counterexample for convergence in L1
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 24th 2009, 11:04 AM
  4. Counterexample
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 28th 2009, 03:06 PM
  5. A counterexample
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: November 1st 2006, 09:06 AM

Search Tags


/mathhelpforum @mathhelpforum