 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/9/a/solution

f : G \to H

preserves the operation:

f (ab) = f (a) f (b)

for all

a, b \in G

. A group isomorphism is a bijective group homomorphism; its inverse also preserves the operation. The kernel of a group homomorphism is

ker f = {g \in G : f (g) = e_{H}}

G

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