The group (U20, X20) = {(1, 3, 7, 9, 11, 13, 17, 19), ×20} has subgroups H = {1,3,7,9} and K = {1,11}. (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. (The standard groups introduced in M208 are listed on pages 136-137 of the Handbook.)

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Chapter2: Second-order Linear Odes
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The group (U20, X20) = {(1, 3, 7, 9, 11, 13, 17, 19), ×20} has
subgroups H = {1,3,7,9} and K = {1, 11}.
(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.
(The standard groups introduced in M208 are listed on pages 136-137
of the Handbook.)
Transcribed Image Text:The group (U20, X20) = {(1, 3, 7, 9, 11, 13, 17, 19), ×20} has subgroups H = {1,3,7,9} and K = {1, 11}. (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. (The standard groups introduced in M208 are listed on pages 136-137 of the Handbook.)
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