some aspects of certain automorphism groups of finite p-groups

Let g be a group and autφ(g) denote the normal subgroup of aut(g), consisting of all automorphisms which act trivially on the factor group g/φ(g). in the present paper, we introduce a new subgroup of autφ(g) for a finite p-group g, and then we study some equalities of this group by some subgroups of the automorphism group of a finite p-group g