Minimal normal implies elementary abelian in finite solvable group

Statement

In a finite solvable group, any minimal normal subgroup is elementary Abelian.

Related facts

Similar facts for other kinds of groups

• Minimal normal implies characteristically simple
• Minimal normal implies additive group of a field in solvable
• Minimal normal implies central in nilpotent
• Minimal normal implies contained in Omega-1 of center for nilpotent p-group
• Minimal normal implies pi-group or pi'-group in pi-separable

Similar facts for maximal normal subgroups

• Maximal normal implies prime index in solvable

Facts used

1. Minimal normal implies characteristically simple
2. Solvable and characteristically simple implies additive group of a field
3. Additive group of a finite field equals elementary Abelian