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- 9. Find all homomorphic images of the octic 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.Find the normalizer of the subgroup (1),(1,3)(2,4) of the octic group D4.
- Find the right regular representation of G as defined Exercise 11 for each of the following groups. a. G={ 1,i,1,i } from Example 1. b. The octic group D4={ e,,2,3,,,, }.Let G be a group with center Z(G)=C. Prove that if G/C is cyclic, then G is abelian.3. Consider the group under addition. List all the elements of the subgroup, and state its order.