Additive group of a field implies characteristic in holomorph

Statement
Suppose $$G$$ is isomorphic to the fact about::additive group of a field. Equivalently, $$G$$ is a fact about::characteristically simple group that is also an abelian group. In particular, $$G$$ is either an fact about::elementary abelian group or a direct sum of copies of the rationals.

Then, $$G$$ is a fact about::characteristic subgroup in its holomorph.

Related facts

 * Characteristically simple and non-abelian implies automorphism group is complete
 * Characteristically simple implies CSCFN-realizable

Facts used

 * 1) uses::Additive group of a field implies monolith in holomorph
 * 2) uses::Monolith is characteristic

Proof using given facts
The proof follows from facts (1)-(2).