Abstract
ABSTRACTLet 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 such that . Also, for a finite non-Abelian p-group G satisfying a certain natural hypothesis, we give some necessary and sufficient conditions for . Furthermore, for a finite non-Abelian p-group G, we study the equality of Autcent(G) with .
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