Kour, SurjeetSurjeetKourSharma, VishakhaVishakhaSharma2025-08-302025-08-302017-02-0110.1080/00927872.2016.11755862-s2.0-84992163484https://d8.irins.org/handle/IITG2025/21778Let 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 (Formula presented.) such that (Formula presented.). Also, for a finite non-Abelian p-group G satisfying a certain natural hypothesis, we give some necessary and sufficient conditions for (Formula presented.). Furthermore, for a finite non-Abelian p-group G, we study the equality of Autcent(G) with (Formula presented.).falseCentral automorphism | class preserving automorphism | finite group | p-groupArticle15324125552-5601 February 20171arJournal1