In this note, we construct countable, torsion-free, amenable, weakly mixing groups, which answer a question of V. Bergelson. Some results related to verbal subgroups and crystallographic groups are also presented.
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Rostislav Grigorchuk, Rostyslav Kravchenko, Alexander Yu. Olshanskii, Constructions of torsion-free countable, amenable, weakly mixing groups. Enseign. Math. 61 (2015), no. 3/4, pp. 321–342DOI 10.4171/LEM/61-3/4-3