3.I.2D

Define what it means for a group to be cyclic. If $p$ is a prime number, show that a finite group $G$ of order $p$ must be cyclic. Find all homomorphisms $\varphi: C_{11} \rightarrow C_{14}$, where $C_{n}$ denotes the cyclic group of order $n$. [You may use Lagrange's theorem.]

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