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(13) The operation table for Do, the dihedral group of order 12, is given in Table 27.6 Table 27.6 Operation table for D (a)
Give a necessary condition on a group G if G/N is a non-Abelian group. Is th essary condition sufficient as well? Explain.
(13) The operation table for Do, the dihedral group of order 12, is given in Table 27.6 Table 27.6 Operation table for D (a) Find the elements of the set Ds/Z(Ds). (b) Write the operation table for the group De/Z(D6) (c) The examples of quotient groups we have seen so far have all been Abelian groups.Is it true that every quotient group is Abelian? Explain.
Give a necessary condition on a group G if G/N is a non-Abelian group. Is th essary condition sufficient as well? Explain.
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