Exercise 4.2.5. Let q: Z6 → Z2 × Z3 be the map p([k]6) ([k]2, [k]3). (1) Show p is well-defined. (2) Show p is a homomorphism. (3) Show p is injective. Why is this enough to conclude q is an isomorphism? Φ =
Exercise 4.2.5. Let q: Z6 → Z2 × Z3 be the map p([k]6) ([k]2, [k]3). (1) Show p is well-defined. (2) Show p is a homomorphism. (3) Show p is injective. Why is this enough to conclude q is an isomorphism? Φ =
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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![Exercise 4.2.5. Let q: Z6 → Z2 × Z3 be the map
q([k]6) = ([k]2, [k]3).
(1) Show p is well-defined.
(2) Show p is a homomorphism.
(3) Show q is injective. Why is this enough to conclude q is an isomorphism?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F833bf7b1-3e6b-4749-8e88-54090320a3f5%2Fd2480485-0a50-459c-b702-6f52ab149d43%2Fp4pjr3_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 4.2.5. Let q: Z6 → Z2 × Z3 be the map
q([k]6) = ([k]2, [k]3).
(1) Show p is well-defined.
(2) Show p is a homomorphism.
(3) Show q is injective. Why is this enough to conclude q is an isomorphism?
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