Let G be a group and let N ≤ G be a normal subgroup. (i) Define...

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 a group.

(ii) Let G = S4, N = K4 = h(1, 2)(3, 4),(1, 3)(2, 4)i ≤ S4. Show that N is a normal subgroup of G and write out the set of cosets G/N.

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Colby Messinger answered 1 year ago

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