Kour, SurjeetSurjeetKourVishakha2025-08-282025-08-282015-05-01http://repository.iitgn.ac.in/handle/IITG2025/20018Let G=H�A be a finite 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 ?:Aut?n(G)Z(G)(G)?Aut?n(H)Z(H)(H) such that ?(Autn?1c(G))=Autn?1c(H). We also give some necessary and sufficient conditions on a finite p-group G such that Autcent(G)=Autn?1c(G) . Furthermore, for a finite non-abelian p-group G, we give some necessary and sufficient conditions for Aut?n(G)Z(G)(G) to be equal to AutZ(G)?2(G)(G).en-USAutomorphism GroupsGroup Theorye-Printe-Print123456789/555