Prove that the factor group Z/4Z is a cyclic group,where Z is the additive group of integers andᏎᏃ={4n: n E Z}

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Answered: Prove that the factor group Z/4Z is a…

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 24E

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Prove that the factor group Z/4Z is a cyclic group, where Z is the additive group of integers and ᏎᏃ = {4n: n E Z}