NONINNER AUTOMORPHISMS OF FINITE p-GROUPS LEAVING THE CENTER ELEMENTWISE FIXED

A longstanding conjecture asserts that every finite nonabelian p-group admits a noninnerautomorphism of order p. let g be a finite nonabelian p-group. it is known that if g is regular orof nilpotency class 2 or the commutator subgroup of g is cyclic, or g=z(g) is powerful, then g hasa noninner automorphism of order p leaving either the center z(g) or the frattini subgroup (g) ofg elementwise fixed. in this note, we prove that the latter noninner automorphism can be chosen sothat it leaves z(g) elementwise fixed.