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
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
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