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- 4. Prove that the special linear group is a normal subgroup of the general linear group .27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.9. Find all homomorphic images of the octic group.
- 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?27. Suppose is a normal subgroup of order of a group . Prove that is contained in , the center of .43. Suppose that is a nonempty subset of a group . Prove that is a subgroup of if and only if for all and .