I need help with #8. Thanks 3.5. CYCLIC GROUPS 3. Give the subgroup diagrams of

Question

I need help with #8. Thanks

3.5. CYCLIC GROUPS 3. Give the subgroup diagrams of the following (a) Z24 (b) Z36 4. Give the subgroup diagram of Zoo- 5.t Find the cyclic subgroup of C* generated by 6. Find the order of the cyclic subgroup of Cx 7.f which of the multiplicative groups Z, , 8. Find (T) in R*. 9:t Find all cyclic subgroups of Z4 x Z2. 10. Find all cyclic subgroups of Zgx Z3 11. Which of the multiplicative groups Z7,Z10.2 12. Let a, b be positive integers, and let d = gcd( 15 18 sition 3.5.5 to prove that Za Zb = Zd × Zm 13. Show that in a finite cyclic group of order n, solutions, for each positive integer m that is a c 14. Prove that any cyclic group with more than tw

Explanation / Answer

Since pi belongs to R. Hence the cyclic subgroup generated by pi is <pi> = { (pi)^n : n belongs to Z}

That is <pi> = { 1, pi, 1/pi, pi^2 , 1/pi^2, .... }

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