Cyclic Group

Moved to abstract algebra... Sorry

Quote:

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Originally Posted by jzellt

Let G1 and G2 be groups and let f: G1 -> G2 be an isomorphism.
If G1 is a cyclic group with generator a, prove that G2 is also a cyclic group, with generator f(a).

Can someone please show this proof? Thanks so much!!!

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This isn't analysis. But, if $\displaystyle g\in G_2$ then $\displaystyle g=f\left(a^n\right)=f^n(a)$ for some $\displaystyle n\in\mathbb{N}$.

Thanks and sorry. I didn't mean to put it in this forum