On Finite p-Groups Whose Central Automorphisms are all Class Preserving

We obtain certain results on a finite p-group whose central automorphisms are all class preserving. In particular, we prove that if G is a finite p-group whose central automorphisms are all class preserving, then d(G) is even, where d(G) denotes the number of elements in any minimal generating set for G. As an application of these results, we obtain some results regarding finite p-groups whose automorphisms are all class preserving.