Let G be a group and let N ? G be a normal subgroup.
(i) Define the factor group G/N and show that G/N is agroup.
(ii) Let G = S4, N = K4 = h(1, 2)(3, 4),(1, 3)(2, 4)i ? S4. Showthat N is a normal subgroup of G and write out the set of cosetsG/N.
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