If $ \phi $ is a homomorphism from G to H and $ \sigma $ is a homomorphism from H to K, show that $ \sigma\phi $ is a homomorphism from G to K.
for this problem you need to show that $ \sigma $($ \phi $(a*b))=$ \sigma $($ \phi $(a))*$ \sigma $($ \phi $(b)).
The left hand side is in G and the right is in K. To prove this you must show a middle step that is created in H by applying the $ \phi $ to a*b to get $ \sigma $($ \phi $(a*b))=$ \sigma $($ \phi $(a)*$ \phi $(b)).
Similarly, the same property can be applied to get to the final step. --Podarcze 12:12, 18 February 2009 (UTC)
