Odd-order elementary abelian group is fully invariant in holomorph

Statement
Let $$p$$ be an odd prime and consider the fact about::elementary abelian group $$G = C_p \times C_p \times \dots \times C_p$$ with the product taken $$r$$ times. Then, $$G$$ is a fact about::fully invariant subgroup inside its holomorph.

Facts used

 * 1) uses::Additive group of a field implies monolith in holomorph
 * 2) uses::Monolith is fully invariant in co-Hopfian group (and in particular, in a finite group).

Proof
The proof follows from facts (1) and (2), along with the observations that: (i) any elementary abelian group is the additive group of a field, so we can use (1), and (ii) the holomorph of a finite group is again finite, so we can use (2).