Finite $p$-groups of class 2 have noninner automorphisms of order $p$

Abstract

We prove that for any prime number $p$, every finite non-abelian $p$-group $G$ of class 2 has a noninner automorphism of order $p$ leaving either the Frattini subgroup $\Phi (G)$ or ${\Omega }_1(Z(G))$ elementwise fixed.

arXiv comment6 pages. to appear in Journal of Algebra