Question: Let G be the group Z 1 0 ? ? under the operation of multiplication modulo 10. 1. List the elements of G 2. What

Let G be the groupZ10?? under the operation of multiplication modulo 10.

1. List the elements of G

2. What is the order of G?

3. Determine the set

4. Determine the set

5. Is G cyclic? Why or why not?

6. Show that 3 and 7 are generators of G

7. What is DLogG,3?(7)?

8. What isDLogG,7?(9)

Let G be the group Z 1 0 ? ? under the operation

Problem 1 [10 points] Let G be the group Zfo under the operation of multiplication modulo 10. 1. List the elements of G 2. What is the order of G? 3. Determine the set (3) 4. Determine the set (9) 5. Is G cyclic? Why or Why not? 6. Show that 3 and 7 are generators of G 7. What is DLogG,3(7)? 8. What is DLogG,7(9)

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