Question 5 (Units B2 and B4) - 17 marks (a) Consider the mapping 0 : 53 53 (i) By writing down the image under @ of each element of S,, show that + is one-to-one and onto. [2] (ii) By demonstrating that there exist permutations p and q in Ss such that o(poq) # o(p) @(q), show that o is not an isomorphism. [4] (b) Now let (G, o) be any group, and let @ be the mapping 0 : G - G (i) Prove that o is one-to-one and onto. 14 (ii) Prove that @ is an isomorphism if and only if G is abelian. 17