i need a and b answer i will 10 upvotes. Problem 8. Suppose that G = (a) is an infinite cyclic group.a) Prove that every non-identity element of G has infinite order.b) For what integers n is an a generator of G? Justify your response.

Suppose that G = <a> is an infinite cyclic group.a) Prove that every non-identity element of G…

Answered: Problem 8. Suppose that G = (a) is an…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.4: Cyclic Groups

Problem 34E

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Problem 8. Suppose that G = (a) is an infinite cyclic group. a) Prove that every non-identity element of G has infinite order. b) For what integers n is an a generator of G? Justify your respon