7.8, due on Novermber 21

I feel similarly about this section as I did about the section on the First Isomorphism Theorem for rings. It was interesting, but the proofs were long and confusing. I didn't understand the proof of theorem 7.45 and since the proof of the First Isomophism Theorem for rings confused me the first time, I would love to run through the proof of the First Isomorphism Theorem for Groups in full instead of just saying "translate the proof of theorem 6.13".

I really liked the Third Isomorphism Theorem for Groups. I thought it was interesting that the book defined another isomorphism theorem in the section rather that just having us discover it in the practices (like in the section about rings). Is that because this theorem is more useful in groups than in rings?