Exercises:Exercise1: Let 0 # a ER and let G = {na| n EZ}. Then (G,+) is anabelian group.(Hint: the identity element is 0 = 0a e G. And the inverse of anyelement na EG is -(na) = (-n)a E G)

Given - Let 0≠a∈ℝ and let G = na | n∈ℤ To Prove : Then G, + is an abelian group. Definition used…

Answered: Exercises: Exercise1: Let 0 # a ER and…

Exercises: Exercise1: Let 0 # a ER and let G = {na| n EZ}. Then (G,+) is an |3D abelian group. (Hint: the identity element is 0 = 0a e G. And the inverse of any element na e G is –(na) = (-n)a E G)

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 14E: 14. Let be an abelian group of order where and are relatively prime. If and , prove that .

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Exercises:
Exercise1: Let 0 # a ER and let G = {na| n EZ}. Then (G,+) is an
abelian group.
(Hint: the identity element is 0 = 0a e G. And the inverse of any
element na EG is -(na) = (-n)a E G)

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