# Outer automorphism group of periodic nilpotent group is direct product of outer automorphism groups of Sylow subgroups

From Groupprops

## Statement

Suppose is a periodic nilpotent group. We know that this means that is a restricted external direct product of nilpotent p-groups. The outer automorphism group of is isomorphic to the (unrestricted) external direct product of the outer automorphism groups of each of the nilpotent -groups.