Minimal normal implies additive group of a field in solvable group

Statement

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

Related facts

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. Minimal normal implies characteristically simple
2. Equivalence of definitions of additive group of a field