The task is to find all the Homomorphisms from group $\mathbb{Z}_{20}$ to $\mathbb{Z}_{16}$. My teacher told be that there is an sufficient way to do this, however I've just brute forced it. Do you have any ideas? Would be grateful for the answer also, just to check my own one.
2026-03-28 11:15:17.1774696517
Find homomorphism between groups
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Several ideas that might be easier than brute force.
Since the domain is a cyclic group, every homomorphism is determined by where it sends a generator. What are the possibilities?
The quotient of the domain modulo the kernel of a homomorphism will be isomorphic to a subgroup of the codomain.