What's that supposed to mean? It's a typo I guess.Where I went wrong was with the fact that i forgot that all cycles abelian
This is not true. (123)² = (321). (123)³ = e (identity). (123)^{4} = (123)³(123) = e(123) = (123) which is not e. Note that this agrees with what I previously mentioned that a k-cycle has order k, since we see the 3-cycle (123) is such that (123)³ = e.Now, I noticed that (123) squared is (321), and cubed is (123) again.