Tonio, I'm not sure if this is the same thing as what you've posted but i've worked on this problem for over an hour and I know now that I can simply show that f is in isomorphism in a map defined f: H x K -> G by f((h,k)) = hk (Where hk is in G).
Does this seem correct so far? This is where I am having my trouble. I worked on one isomorphism problem similar to this before but I cant seem to apply any of the same methods or logic to this one.
How do I show f is an isomorphism in this problem?