Theorem Proof Let f: G→→ H be a group homomorphism. Then, Im fs H. The kernel of f, we write Ker f, is Ker f= {ge G: f(g) = en}. The Image of f, we write Im f, is Im f= {he H: h= f(g) for some g = G).
Theorem Proof Let f: G→→ H be a group homomorphism. Then, Im fs H. The kernel of f, we write Ker f, is Ker f= {ge G: f(g) = en}. The Image of f, we write Im f, is Im f= {he H: h= f(g) for some g = G).
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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![Theorem
Let f: G → H be a group homomorphism. Then, Im fs H.
Proof
The kernel of f, we write Ker f, is
Ker f = {g e G: f(g) = en}.
The Image of f, we write Im f, is
Im f= {h e H: h = f(g) for some g e G}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F599f7899-35c5-46e7-852c-1de16debf569%2Fdae0d6cc-2519-4fc5-8a12-7665f11bcf63%2Fpkqpne_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Theorem
Let f: G → H be a group homomorphism. Then, Im fs H.
Proof
The kernel of f, we write Ker f, is
Ker f = {g e G: f(g) = en}.
The Image of f, we write Im f, is
Im f= {h e H: h = f(g) for some g e G}.
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