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CSS Pure Mathematics QUESTION #4131
Question 1
If $\varphi: \mathbb{Z}_{12} \to \mathbb{Z}_{18}$ is a group homomorphism, how many exist?
  • $6$
  • $4$
  • $12$
  • $\gcd(12, 18) = 6$✔️
Correct Answer Explanation
Number of homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$ equals $\gcd(m, n) = \gcd(12, 18) = 6$.