7.8

1. Composition factors look interesting and deep. I wouldn't mind another explanation of them.

2. I think the real insight here is in the definitions of kernel, the homomorphic mapping from one group to another, the standardization of these theorems and definitions. These are given freely and then the proofs are relegated to previous results in analogous ring constructs. I suppose this is a good thing, since, while the definitions and homomorphisms seem trivial, it is easy to see these things after the fact.