On equality of certain subcentral automorphisms in finite p-groups

Abstract

Let [Formula: see text] be a group and [Formula: see text] be the group of all automorphisms of [Formula: see text]. In this paper, we study the structure of certain subgroups of the automorphisms group [Formula: see text] and give necessary and sufficient conditions for equality between certain subcentral automorphisms. As consequence of these results, we state a number of interesting corollaries about central automorphisms, autocentral automorphisms and derival automorphisms for finite [Formula: see text]-groups.