Question: (6) Let n E N such that n 2 3. Prove that the center Z (Sn ) is the trivial group. (Hint: Con- sider a

(6) Let n E N such that n 2 3. Prove that the center Z (Sn ) is the trivial group. (Hint: Con- sider a nonidentity element o E Sn and two distinct numbers a, be {1, 2, ..., n} such that o(a) = b. Fix another number c E {1, 2, ..., n}, c # a, c # b. Construct a permutation T such that or * To.)

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