Let N, K be two normal subgroups of a group G. Show that NK is a normal subgroup of G.
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- 27. Suppose is a normal subgroup of order of a group . Prove that is contained in , the center of .Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?