I know full well the proof using Lagrange's thm. But is there a direct way to do this without using the fact that the order of an element divides the order of the group?(adsbygoogle = window.adsbygoogle || []).push({});

I was thinking there might be a way to set up an isomorphism directly between G and Z/pZ.

Clearly all non-zero elements of Z/pZ are generators, so sending any non-identity element of G to any equivalence class of 1,...,p-1 should induce an isomorphism... but how to prove it?

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# Groups of prime order are cyclic. (without Lagrange?)

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