Can you explain to me how this works? Specifically, how does the permutation multiplication work. How…

Can you explain to me how this works? Specifically, how does
the permutation multiplication work. How does (1,3,4,6)(2,3,5)
become the 2 permutations multiplied together. I guess I am lost on
all of it.

4. Let T = (1,3,4,6)(2,3,5) in Ss. Find the index of in So. S61 Solution: If we let H = (r), then we are looking for (S. : H) However, we cannot simply claim that H = 12 because the cycle decomposition for T is not disjoint. Therefore, we need to figure out what the actual disjoint cycle decomposition is. To do that, we need to figure out what is as a permutation, not the given cycles. To do this, just multiply the permutations out 3 4 5 6 1 2 3 4 5 6 3 5 4 2 6 4 5 6 2 1 TE 2 = (1,3,4,6)(2,3,5) = (338 56 1 3 1) Following the process we did in problem 3 to break down into its cycle decomposition, we see that T=(1,3,5, 2, 1,6) and is itself a cycle of length 6. Therefore, |M| -6 and (S6: H) 6! 120. 6