Cardinality of Finite Fields
Achyut BharadwajSeptember 2022
cardinality,
finite field,
automorphism,
characteristic,
isomorphism,
homomorphism,
Fermat's Little Theorem,
FLT
Introduction #
A well known theorem about finite fields states the following.
$F$ is a finite field if and only if $|F| = p^k$ for some prime $p$ and positive integer $k$.
In this write-up, we prove the first part of the above theorem, i.e. if $F$ is a finite field, then $|F| = p^k$ using a different approach.
Introduction to Finite Fields #
We first list down some basic definitions that will be used as we move forward in this write-up.
...