Algebra I – autumn 2024 – Homework 5
1. Decide whether f : (Z6, +) → (Z×
7 , ·), f([a]6) = [3]a
7 defines a map. If so, decide whether it is a
group homomorphism or even an isomorphism.
2. Give an example of a group G and a non-injective group homomorphism φ: G → G whose kernel
is equal to its image.