P-groups for which each outer p-automorphism centralizes only p elements

Abstract

An automorphism of a group is called outer if it is not an inner automorphism. Let G be a finite p-group. Then for every outer p-automorphism Φ of G the subgroup CG(Φ) = {x∈G | xΦ = x} has order p if and only if G is of order at most p2.