Cyclic group of prime power order has algebraic group structure over corresponding prime field

Statement
(Note that the statement also holds for the trivial group, but that is not an interesting case).

Suppose $$p$$ is a prime number and $$n$$ is a natural number. Then the fact about::cyclic group of prime power order $$p^n$$ can be naturally given the structure of an fact about::algebraic group over the prime field $$\mathbb{F}_p$$.

Facts used

 * 1) uses::Additive group of ring of Witt vectors inherits algebraic group structure