Struggling to understand a field theorm's corollary

Theorem: Let F be any field. If G is a finite subgroup of the multiplicative group F* of F, then G is cyclic. In particular, is F is finite, then F* is cyclic.



Corolarry 1: GF(p^n) = Z_p(u), where u is any primitive element for GF(p^n).



So <u> = GF(p^n)*, so |u| = GF(p^n) - 1.



I'm now trying...



Struggling to understand a field theorm's corollary

Struggling to understand a field theorm's corollary