# Minimal normal implies contained in Omega-1 of center for nilpotent p-group

From Groupprops

## Statement

In a Nilpotent p-group (?) , any Minimal normal subgroup (?) is contained in the subgroup (the first omega subgroup of the center of ). Thus, the Socle (?) of is contained in .
(in fact, something stronger is true: for a nilpotent p-group, the socle *equals* Omega-1 of the center).

## Related facts

- Socle equals Omega-1 of center for nilpotent p-group
- Minimal normal implies central in nilpotent
- Minimal characteristic implies central in nilpotent
- Minimal characteristic implies contained in Omega-1 of center for nilpotent p-group