On Finite p-Groups Whose IA-Automorphisms Are All Class Preserving

Let G be a finite non-abelian p-group, where p is a prime. An automorphism of G is called a class preserving automorphism if (x)x(G) the conjugacy class of x in G, for all xG. An automorphism of G is called an IA-automorphism if x(-1)(x)G for each xG. In this paper, we give necessary and sufficient conditions on finite p-group G of nilpotency class 2 such that every IA-automorphism is class preserving.