Constructions of torsion-free countable, amenable, weakly mixing groups
  In this note, we construct torsion-free countable, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallographic groups are also presented. 
Rostislav Grigorchuk and Rostyslav Kravchenko and Alexander Olshanskii
math.DS math.GR