Abstract Algebra I · Cyclic and permutation groups
Images of cyclic groups are cyclic
Problem
Let $\varphi:G\to H$ be a group homomorphism and suppose $G=\langle a\rangle$. Prove $\operatorname{im}\varphi=\langle\varphi(a)\rangle$.
Hint
An image element has the form $\varphi(a^n)$.
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