Algebra and Geometry | Part IA, 2005

Define what it means for a group to be cyclic. If pp is a prime number, show that a finite group GG of order pp must be cyclic. Find all homomorphisms φ:C11C14\varphi: C_{11} \rightarrow C_{14}, where CnC_{n} denotes the cyclic group of order nn. [You may use Lagrange's theorem.]

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