Abstract:
Let G = H×A be a group, where H is a purely non-Abelian subgroup of G, and A is a non-trivial Abelian factor of G. Then, for n≥2, we show that there exists an isomorphism ϕ:Autγn(G)Z(G)(G)→Autγn(H)Z(H)(H) such that ϕ(Autn−1c(G))=Autn−1c(H). Also, for a finite non-Abelian p-group G satisfying a certain natural hypothesis, we give some necessary and sufficient conditions for Autcent(G)=Autn−1c(G). Furthermore, for a finite non-Abelian p-group G, we study the equality of Autcent(G) with Autγn(G)Z(G)(G).