Find S4/N elements and show that they can be combined into a group. N={e,(23),(234),(243),(12)(34), (123), (132), (134),(13)(24), (142),(143),(14)(23)}

(6) Find the order of the following permutations: (a) (154)(254)(1234) E S5.

Suppose a permutation s swaps the first two elements of {1, 2, ..., n}. A permutation r rotates the elements: r(1)=2, r(2)=3, ... r(n-1)=n, r(n)=1. We can thus write in cycle notation: s=(1 2), r=(1 2 3 4 ... n). What does the permutation rm sr -m do?

(a) Write (152) (341) (6352) ≤ S6 in array form. Fill in the blank row below. 1 2 3 4 5 6 (b) Express [ 1 2 3 4 5 6 7 8 9 1 4 2 97 8 5 3 6 as a product of disjoint cycles. (c) How many elements of order 10 does S7 have?