%0 Journal Article
%T Noninner automorphisms of finite p-groups leaving the center elementwise fixed
%A Alireza Abdollahi
%A S. Mohsen Ghoraishi
%J International Journal of Group Theory
%D 2013
%I University of Isfahan
%X A longstanding conjecture asserts that every finite nonabelian p-group admits a noninner automorphism of order p. Let G be a finite nonabelian p-group. It is known that if G is regular or of nilpotency class 2 or the commutator subgroup of G is cyclic, or G/Z(G) is powerful, then G has a noninner automorphism of order p leaving either the center Z(G) or the Frattini subgroup Phi(G) of G elementwise fixed. In this note, we prove that the latter noninner automorphism can be chosen so that it leaves Z(G) elementwise fixed.
%K Noninner automorphism
%K finite p-groups
%K the center
%U http://www.theoryofgroups.ir/?_action=showPDF&article=2761&_ob=dbf6c7e37f884c3d7c270219cb030012&fileName=full_text.pdf.