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QUESTION 6 Let G = {1,-1,i.-i}. Given that G with the operation of multiplication of complex numbers is a group. Define : Z→G by (n) = (-1)" where Zis the group of integers with the operation of addition. a) Show that is a homomorphism. b) Is an isomorphism? Justify your answer.

QUESTION 6 Let G = {1,-1,i.-i}. Given that G with the operation of multiplication of complex numbers is a group. Define : Z→G by (n) = (-1)" where Zis the group of integers with the operation of addition. a) Show that is a homomorphism. b) Is an isomorphism? Justify your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Abstract Algebra I
QUESTION 6 Let G = {1,-1,i.-i}. Given that G with the operation of multiplication of complex numbers is a group. Define : Z→G by (n) = (-1)" where Zis the group of integers with the operation of addition. a) Show that is a homomorphism. b) Is an isomorphism? Justify your answer.
Transcribed Image Text:QUESTION 6 Let G = {1,-1,i.-i}. Given that G with the operation of multiplication of complex numbers is a group. Define : Z→G by (n) = (-1)" where Zis the group of integers with the operation of addition. a) Show that is a homomorphism. b) Is an isomorphism? Justify your answer.
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