1/ Determine in each of the parts if the given mapping is a homomorphism.If so, identify its kernel and whether or not the mapping is 1-1 or onto.(a) G = Z under +, G' = Zn, 4(a) = [a] for a € Z.(b) G group, : G→ G defined by o(a) = a¹ for a E G.1(c) G abelian group, : G→ G defined by (a) = a¹ for a € G.(d) G group of all nonzero real numbers under multiplication, G' ={1, -1), p (r) = 1 if r is positive, (r) = -1 if r is negative.(e) G an abelian group, n >1 a fixed integer, and o: G→ G defined by(a) = a" for a E G.

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Answered: 1/ Determine in each of the parts if…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.6: Quotient Groups

Problem 11E: Find all homomorphic images of the quaternion group.

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