Equality of certain automorphism groups of finite p-groups

Abstract

Let [Formula: see text] be a finite [Formula: see text]-group and let Aut([Formula: see text]) denote the full automorphism group of [Formula: see text]. In the recent past, there has been interest in finding necessary and sufficient conditions on [Formula: see text] such that certain subgroups of Aut([Formula: see text]) are equal. We prove a technical lemma and, as a consequence, obtain some new results and short and alternate proofs of some known results of this type.