Question 9.(a) Prove that every element of Q/Z has finite order.(b) Given two groups (G,) and (H, +). Suppose that is a homomorphism of G onto H. ForBH and A:= {g EG: 0(g) e B), prove that AG.

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 21E

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Question 9. (a) Prove that every element of Q/Z has finite order.