The group (U20, X20) = {(1, 3, 7, 9, 11, 13, 17, 19), ×20} has subgroups H = {1,3,7,9) and K = {1,11}. morphe laun (a) Explain why both H and K are normal subgroups of U20, and for each of H and K list all of its distinct cosets in U20. (b) For each of H and K, write down the group table of its quotient group in U20, and state a standard group to which the quotient group is isomorphic, briefly justifying your answer.

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