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- 45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )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?4. Prove that the special linear group is a normal subgroup of the general linear group .
- 22. If and are both normal subgroups of , prove that is a normal subgroup of .Exercises 3. Find an isomorphism from the additive group to the multiplicative group of units . Sec. 16. For an integer , let , the group of units in – that is, the set of all in that have multiplicative inverses, Prove that is a group with respect to multiplication.10. Find all normal subgroups of the octic group.