Sections 7.9-7.10 Due May 6

1. I don't understand how the product of the cycle groups works.I didn't understand the proof of lemma 7.54, especially when all the sudden they had 12k. I didn't see where that came from.
2. I really liked section 7.9 and thought it was kind of fun, but it seems a little pointless and like something that someone just made up and gave a name. I see no relevance in all of the connections that were made between cycles and the group S_n. They were interesting theorems, but seemed useless.