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Let  G  be a finite  p -group. Letandrespectively denote the group of all absolute central and-automorphisms of  G . We give necessary and sufficient conditions for a finite non-abelian  p -group  G  such thatand as a consequence, we prove that for a finite non-abelian  p -group  G  of order up to  p4 ,if and only ifwhere  L ( G ) denotes the absolute center of  G .

On equality of absolute central and IA-automorphism groups of finite p -groups