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

Statement

In a Nilpotent p-group (?) $G$, any Minimal characteristic subgroup (?) is contained in the subgroup $\Omega _{1}(Z(G))$ (the first omega subgroup of the center of $G$).

Related facts

• Omega-1 of center not is minimal characteristic
• Minimal normal implies central in nilpotent
• Minimal characteristic implies central in nilpotent
• Minimal normal implies contained in Omega-1 of center for nilpotent p-group

Facts used

1. Omega-1 of center is normality-large in nilpotent p-group