I want to prove that two finite field of same order is isomorphic.
I have thought something.
My attempt : If $f$ be a field of order $p ^m $ then $(f,+)$ is $z_p × z_p × .......z_p$.
$(f , .) $ is $z_{p^m - 1}$.
Am I right? Can anyone please check ? If I am right can you please tell how to conclude then?
If I am wrong can you please tell me a trivial way of seeing it. I am a first reader of field theory.