Groups and Permutations Question:

5. Let Sn he the symmetric group of degree n. (a) Write the permutation 1 2 3 4 5 5 7 8 (I: 653 3 7 4 1 3 2 6 5 as a product of disjoint cycles and find its inverse. [4] [b] Find a permutation or in 83 such that or show that no such permutation exists. [4] (c) Write the permutation : [1247)(13453) [1352) as a product of disjoint cycles in SS. [3] 2UMAA242APV/APS continued... 30f3 (d) Compute the signs of the permutations o: and ,6. For each permutation (I and . say whether it can be written as a product of 3cycles in SE. You must justify your answer. [4]