4. Let us define f : Z6 → Zž as f([r]) = [2ª]. Where [.] is the residue class interpreted correctly. (a) Show that f is a homomorphism. (Be careful, the group structure on left is via addition and on the right via multiplication) (b) What is Kernel of this homomorphism?
4. Let us define f : Z6 → Zž as f([r]) = [2ª]. Where [.] is the residue class interpreted correctly. (a) Show that f is a homomorphism. (Be careful, the group structure on left is via addition and on the right via multiplication) (b) What is Kernel of this homomorphism?
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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![4. Let us define f : Z6 → Zž as f([æ]) = [2"]. Where [:) is the residue class interpreted correctly.
(a) Show that f is a homomorphism. (Be careful, the group structure on left is via addition
and on the right via multiplication)
(b) What is Kernel of this homomorphism?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb39617aa-1a85-4ff5-98c6-3f7fe0e80deb%2Fa3f10d33-91d8-41b8-a4ef-8bb045c0194f%2Fgsqjn1_processed.png&w=3840&q=75)
Transcribed Image Text:4. Let us define f : Z6 → Zž as f([æ]) = [2"]. Where [:) is the residue class interpreted correctly.
(a) Show that f is a homomorphism. (Be careful, the group structure on left is via addition
and on the right via multiplication)
(b) What is Kernel of this homomorphism?
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