A math question:

能不能请你们为我的朋友解答一道数学题？

先谢谢了。

given permutation p = (3 4 1)(2 5) and q = (1 4 5 2), both in cycle notation and with permutation product from right to left, we can see that p q and q p result in a 3-cycle. Is this an accident ? If not, what are the properties causing it ?

15 分钟到了。朋友解出了基本走向。 both p and q are odd permutations, so both pq and qp are even。 i can prove that any even permutation can be written as a product of 3-cycles。 so we're very close, we just have to prove that in this case it's just one 3-cycle。 看看有谁能把最后一步解出来不。