1) So if I understand correctly, elements that map to themselves to not add to the length k of the cycle. Can you compose any two groups, even if they have different cycle lengths? Does it all depend on the amount of elements that they have? I really don't understand the factorization of permutations. Both theorem 7.51 and the proof is a little bit difficult.
2) Even though I don't understand it yet, I would say the most interesting part is seeing how they factor permutations.
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