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Homework Help: Onto Homomorphism

  1. Mar 4, 2012 #1
    If G/H is [itex]\cong[/itex] K show there exist an homomorphism which is ont λ:G [itex]\rightarrow[/itex] K with the kernel of λ=H

    I am having a hard time figuring out what this should be. I have a feeling it is easy if you know how to look at it.

    I have been trying the First Isomorphism Theorem but I cant seem to get.

    Any help would e greatly appreciated.
  2. jcsd
  3. Mar 4, 2012 #2


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    You have an isomorphism [itex]\phi : G/H \rightarrow K[/itex]. Can you find a surjective homomorphism [itex]\theta : G \rightarrow G/H[/itex] which has ker [itex]\theta = H[/itex]? What happens when you compose [itex]\theta[/itex] with [itex]\phi[/itex]?
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