Definitions

$⟨$ Definition A-4.1 $⟩$ Order Definition

${𝗈𝗋𝖽}_{𝔽} (𝐚)$ : For $a \in 𝔽$ (a finite field, §A-3.1), $a$ ’s order is the smallest positive integer $k$ such that $a^{k} = 1$ .

Note that the multiplicative group generated by

a

as a generator excludes

{0}

, the identity, because

0^{k} = 0

for all

k

values.