# Cyclic Group

• October 31st 2010, 07:23 PM
jzellt
Cyclic Group
Moved to abstract algebra... Sorry
• October 31st 2010, 07:24 PM
Drexel28
Quote:

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 $n\in\mathbb{N}$.
• October 31st 2010, 07:29 PM
jzellt
Thanks and sorry. I didn't mean to put it in this forum