# Groups : Isomorphism and Homomorphism

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Note: G =~ G1 means G is isomorphic to G1

If G/K =~ H, show that there exists an onto homomorphism $:G -> H with kernel $ = K

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#### Solution Preview

Proof:

Since G/K=~H, then there exists an isomorphism f: G/K->H. For any h in H, we can find a gK in G/K such that ...

#### Solution Summary

Homomorphic groups are investigated.

$2.49