# P-nilpotent implies p-normal

From Groupprops

## Statement

Suppose is a finite group that is a p-nilpotent group, i.e., it has a normal p-complement, or equivalently, the -Sylow subgroup is a retract. Then, is a p-normal group: the center of the Sylow subgroup is a weakly closed subgroup in it.

## Facts used

## Proof

The proof follows directly by combining facts (1) and (2).