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CSS Pure Mathematics QUESTION #4113
Question 1
Let $\varphi: \mathbb{Z}_6 \to \mathbb{Z}_6$ be a group homomorphism. If $\varphi$ is one-to-one (injective), what is $|\ker(\varphi)|$?
  • $0$
  • $1$✔️
  • $6$
  • $\text{Not determined}$
Correct Answer Explanation
For injective homomorphism, kernel contains only identity element. So $|\ker(\varphi)| = 1$.