Automorphisms of finite p-groups

The non-inner automorphism conjecture (NIAC) and the divisibility problem (DP) are two famous problems in the study of finite p-groups. We observe that the verification of NIAC can be reduced to purely non-abelian finite p-groups. In connecting NIAC with DP, as a consequence of our results obtained on NIAC, we provide a short and cohomology-free proof of a theorem of Yadav, which states that if G is a finite p-group such that (G, Z(G)) is a Camina pair, then |G| divides \(|{{\,\mathrm{\!Aut}\,}}(G)|\).