Minimal normal implies additive group of a field in solvable group

Statement
Suppose $$G$$ is a fact about::solvable group and $$H$$ is a fact about::minimal normal subgroup of $$G$$. Then, $$H$$ is isomorphic to the fact about::additive group of a field.

Similar facts

 * Minimal normal implies characteristically simple
 * Minimal normal implies elementary abelian in finite solvable
 * Minimal normal implies pi-group or pi'-group in pi-separable
 * Minimal normal implies central in nilpotent

Facts used

 * 1) uses::Minimal normal implies characteristically simple
 * 2) uses::Equivalence of definitions of additive group of a field