Source: /cirosantilli/classification-of-finite-fields

= Classification of finite fields
{tag=Classification (mathematics)}

There's exactly one field per <prime power>, so all we need to specify a field is give its order, notated e.g. as $GF(n)$.

Every element of a finite field satisfies $x^{order} = x$.

It is interesting to compare this result philosophically with the <classification of finite groups>: fields are more constrained as they have to have two operations, and this leads to a much simpler classification!