Multiplicative Group of Galois Field is Cyclic

Theorem

Let $\GF$ be a Galois field of order $q$.

Then its multiplicative group is cyclic of order $q-1$:

$\GF^\times \cong C_{q - 1}$

Proof

Follows immediately from Finite Multiplicative Subgroup of Field is Cyclic.

$\blacksquare$