Minimal Abelian groups that are not automorphism groups (Q1127963)

This paper deals with abelian \(p\)-groups of minimal order which can occur as the automorphism group of a finite group. In particular the authors prove that if \(G\) is a non-cyclic group of order \(p^7\) and \(\Aut G\) is abelian, then \(\Aut G\) must be of order \(p^{12}\). Moreover, there is no group \(G\) such that \(\Aut G\) is an abelian \(p\)-group of order \(p^{11}\) (where \(p>2\)).