Cyclic Group

**jzellt** · October 31st 2010, 07:23 PM

Moved to abstract algebra... Sorry

**Drexel28** · October 31st 2010, 07:24 PM

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!!!

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

**jzellt** · October 31st 2010, 07:29 PM

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

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