I have the following question :
Find all non-trivial homomorphism $\mathbb{Z_{14}}\rightarrow \mathbb{Z_{21}}$ I wonder how to solve such problems when the groups are pretty big to check the definition of each possibility.
Any ideas?
Thank you.
Method of finding all non-trivial homomorphism $\mathbb{Z_{14}}\rightarrow \mathbb{Z_{21}}$
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abstract-algebra
group-theory
group-homomorphism
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0Have you thought about the image of such a homomorphism? Probably you have some theorems about that. – 2017-01-30
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1If $C$ is a cyclic group generated by $\sigma$ and $G$ is any other group then homomorphisms $C\to G$ correspond to places to send $\sigma$ to... – 2017-01-30
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1Also an answer [here](http://math.stackexchange.com/questions/45663/quick-way-to-find-the-number-of-the-group-homomorphisms-phi-bf-z-3-to-bf-z). – 2017-01-30
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0$\phi : \mathbb{Z}_n \to G$ is an homomorphism iff $ord(\phi(1)) \ \mid \ n$, and it is non-trivial iff $ord(\phi(1)) > 1$. – 2017-01-30