Some new non-Abelian 2-groups with Abelian automorphism groups (Q2776800)

The goal of the paper under review is to exhibit, for any integers \(m\geq 2\), \(n\geq 3\), a non-Abelian, \(n\)-generator group of order \(2^{2n+m-2}\) and exponent \(2^m\) whose automorphism group is isomorphic to the direct product of an elementary Abelian group of order \(2^{n^2}\) with the cyclic group of order \(2^{m-2}\). This shows that the number of generators and the exponent of a finite non-Abelian \(2\)-group with an Abelian automorphism group can be arbitrarily large. The examples are constructed in a neat direct fashion.