Onto Homomorphism

1. Mar 4, 2012

Punkyc7

If G/H is $\cong$ K show there exist an homomorphism which is ont λ:G $\rightarrow$ 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. Mar 4, 2012

jbunniii

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