Exercise 3. Let T be a set such that |T| ≥ 3 and let G = Sym(T) be the group of permutations of T. (i) For each pair a b € T, define fa,b E G by b, fa,b(t) = a, t, G|{g(a), g(b)} = {a,b}}. if t = a; if t = b; Prove that C(fa,b) = {g (ii) Prove that Z(G) = {I}. otherwise.

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