Misbehaved direct products
The author presents with leisurely discussion 3 deceptively difficult open problems concerning direct products of groups. The first is whether the direct product of a Hopfian group and the infinite cyclic group is necessarily Hopfian. The second is whether a finitely presented group can be a proper direct factor of itself. The third (labelled ``for quick fame'') is more technical and related to the Poincaré conjecture.
scientific article; zbMATH DE number 1870161
scientific article